Relevant bibliographies by topics / Gaussian quantum mechanics

Academic literature on the topic 'Gaussian quantum mechanics'

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Published: 1 June 2024

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Gaussian quantum mechanics":

1

ACOSTA, D., P. FERNÁNDEZ DE CÓRDOBA, J. M. ISIDRO, and J. L. G. SANTANDER. "EMERGENT QUANTUM MECHANICS AS A CLASSICAL, IRREVERSIBLE THERMODYNAMICS." International Journal of Geometric Methods in Modern Physics 10, no. 04 (March 6, 2013): 1350007. http://dx.doi.org/10.1142/s0219887813500072.

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We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.
2

Sankovich, D. P. "Bogolyubov Gaussian Measure in Quantum Statistical Mechanics." Universal Journal of Physics and Application 13, no. 2 (March 2019): 29–41. http://dx.doi.org/10.13189/ujpa.2019.130201.

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Simon, R., E. C. G. Sudarshan, and N. Mukunda. "Gaussian-Wigner distributions in quantum mechanics and optics." Physical Review A 36, no. 8 (October 1, 1987): 3868–80. http://dx.doi.org/10.1103/physreva.36.3868.

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KHRENNIKOV, ANDREI. "QUANTUM CORRELATIONS FROM CLASSICAL GAUSSIAN RANDOM VARIABLES: FUNDAMENTAL ROLE OF VACUUM NOISE." Fluctuation and Noise Letters 09, no. 04 (December 2010): 331–41. http://dx.doi.org/10.1142/s0219477510000265.

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We show that, in spite of rather common opinion, correlations of observables on subsystems of a composite quantum system can be represented as correlations of classical Gaussian variables. We restrict our model to the finite dimensional case (which is important, e.g., in quantum information theory). Here quantum correlations are represented by integrals with Gaussian densities which can be directly calculated. In particular, the EPR–Bell correlations for polarizations of entangled photons can be represented as correlations of Gaussian random variables. The tricky point of our construction is the necessity to introduce the Gaussian noise ("vacuum fluctuations") to obtain positively defined covariance matrices for "prequantum random variables." Quantum mechanics can be considered as a method to proceed by subtracting the influence of this Gaussian background noise.
5

Przhiyalkovskiy, Y. V. "Quantum process in probability representation of quantum mechanics." Journal of Physics A: Mathematical and Theoretical 55, no. 8 (February 1, 2022): 085301. http://dx.doi.org/10.1088/1751-8121/ac4b15.

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Abstract In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit flipping and amplitude damping processes.
6

ALAVI, S. A. "SCATTERING IN NONCOMMUTATIVE QUANTUM MECHANICS." Modern Physics Letters A 20, no. 13 (April 30, 2005): 1013–20. http://dx.doi.org/10.1142/s021773230501697x.

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We derive the correction due to noncommutativity of space on Born approximation, then the correction for the case of Yukawa potential is explicitly calculated. The correction depends on the angle of scattering. Using partial wave method, it is shown that the conservation of the number of particles in elastic scattering is also valid in noncommutative spaces which means that the unitarity relation is held in noncommutative spaces. We also show that the noncommutativity of space has no effect on the optical theorem. Finally we study Gaussian function potential in noncommutative spaces which generates delta function potential as θ → 0.
7

Iomin, Alexander, Ralf Metzler, and Trifce Sandev. "Topological Subordination in Quantum Mechanics." Fractal and Fractional 7, no. 6 (May 25, 2023): 431. http://dx.doi.org/10.3390/fractalfract7060431.

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An example of non-Markovian quantum dynamics is considered in the framework of a geometrical (topological) subordination approach. The specific property of the model is that it coincides exactly with the fractional diffusion equation, which describes the geometric Brownian motion on combs. Both classical diffusion and quantum dynamics are described using the dilatation operator xddx. Two examples of geometrical subordinators are considered. The first one is the Gaussian function, which is due to the comb geometry. For the quantum consideration with a specific choice of the initial conditions, it corresponds to the integral representation of the Mittag–Leffler function by means of the subordination integral. The second subordinator is the Dirac delta function, which results from the memory kernels that define the fractional time derivatives in the fractional diffusion equation.
8

Schnabel, Roman, and Mikhail Korobko. "Macroscopic quantum mechanics in gravitational-wave observatories and beyond." AVS Quantum Science 4, no. 1 (March 2022): 014701. http://dx.doi.org/10.1116/5.0077548.

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The existence of quantum correlations affects both microscopic and macroscopic systems. On macroscopic systems, they are difficult to observe and usually irrelevant for the system's evolution due to the frequent energy exchange with the environment. The world-wide network of gravitational-wave (GW) observatories exploits optical as well as mechanical systems that are highly macroscopic and largely decoupled from the environment. The quasi-monochromatic light fields in the kilometer-scale arm resonators have photon excitation numbers larger than 1019, and the mirrors that are quasi-free falling in propagation direction of the light fields have masses of around 40 kg. Recent observations on the GW observatories LIGO and Virgo clearly showed that the quantum uncertainty of one system affected the uncertainty of the other. Here, we review these observations and provide links to research goals targeted with mesoscopic optomechanical systems in other fields of fundamental physical research. These may have Gaussian quantum uncertainties as the ones in GW observatories or even non-Gaussian ones, such as Schrödinger cat states.
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MUÑOZ-TAPIA, R., J. TARON, and R. TARRACH. "THE UNCERTAINTY OF THE GAUSSIAN EFFECTIVE POTENTIAL." International Journal of Modern Physics A 03, no. 09 (September 1988): 2143–63. http://dx.doi.org/10.1142/s0217751x88000898.

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An uncertainty is introduced for the Gaussian Effective Potential. The definition is quite straightforward for quantum mechanics but fairly subtle for quantum field theory. The uncertainty provides a good estimation of the error in the first case, but renormalization seems to spoil its usefulness in the second case. The examples considered are the anharmonic oscillator, λϕ4 in 3+1 dimensions and the Liouville theory in 1+1 dimensions.
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Lasser, Caroline, and Christian Lubich. "Computing quantum dynamics in the semiclassical regime." Acta Numerica 29 (May 2020): 229–401. http://dx.doi.org/10.1017/s0962492920000033.

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The semiclassically scaled time-dependent multi-particle Schrödinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This paper reviews and studies numerical approaches that are robust to the small semiclassical parameter. We present and analyse variationally evolving Gaussian wave packets, Hagedorn’s semiclassical wave packets, continuous superpositions of both thawed and frozen Gaussians, and Wigner function approaches to the direct computation of expectation values of observables. Making good use of classical mechanics is essential for all these approaches. The arising aspects of time integration and high-dimensional quadrature are also discussed.
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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Gaussian quantum mechanics":

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Coughtrie, David James. "Gaussian wave packets for quantum statistical mechanics." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682558.

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Thermal (canonical) condensed-phase systems are of considerable interest in computational science, and include for example reactions in solution. Time-independent properties of these systems include free energies and thermally averaged geometries - time-dependent properties include correlation functions and thermal reaction rates. Accounting for quantum effects in such simulations remains a considerable challenge, especially for large systems, due to the quantum nature and high dimensionality of the phase space. Additionally time-dependent properties require treatment of quantum dynamics. Most current methods rely on semi-classical trajectories, path integrals or imaginary-time propagation of wave packets. Trajectory based approaches use continuous phase-space trajectories, similar to classical molecular dynamics, but lack a direct link to a wave packet and so the time-dependent schrodinger equation. Imaginary time propagation methods retain the wave packet, however the imaginary-time trajectory cannot be used as an approximation for real-time dynamics. We present a new approach that combines aspects of both. Using a generalisation of the coherent-state basis allows for mapping of the quantum canonical statistical average onto a phase-space average of the centre and width of thawed Gaussian wave packets. An approximate phase-space density that is exact in the low-temperature harmonic limit, and is a direct function of the phase space is proposed, defining the Gaussian statistical average. A novel Nose-Hoover looped chain thermostat is developed to generate the Gaussian statistical average via the ergodic principle, in conjunction with variational thawed Gaussian wave-packet dynamics. Numerical tests are performed on simple model systems, including quartic bond stretching modes and a double well potential. The Gaussian statistical average is found to be accurate to around 10% for geometric properties at room temperature, but gives energies two to three times too large. An approach to correct the Gaussian statistical average and ensure classical statistics is retrieved at high temperature is then derived, called the switched statistical average. This involves transitioning the potential surface upon which the Gaussian wave packet propagates, and the system property being averaged. Switching functions designed to perform these tasks are derived and tested on model systems. Bond lengths and their uncertainties calculated using the switched statistical average were found to be accurate to within 1% relative to exact results, and similarly for energies. The switched statistical average, calculated with Nose- Hoover looped chain thermostatted Gaussian dynamics, forms a new platform for evaluating statistical properties of quantum condensed-phase systems using an explicit real-time wave packet, whilst retaining appealing features of trajectory based approaches.
2

Bartók-Pártay, Albert. "Gaussian approximation potential : an interatomic potential derived from first principles Quantum Mechanics." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608570.

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Baghery, Mehrdad. "Dynamics of Driven Quantum Systems:." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-232398.

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This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.
4

Yockel, Scott. "The evaluation, development, and application of the correlation consistent basis sets." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5484/.

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Employing correlation consistent basis sets coupled with electronic structure methods has enabled accurate predictions of chemical properties for second- and third-row main group and transition metal molecular species. For third-row (Ga-Kr) molecules, the performance of the correlation consistent basis sets (cc-pVnZ, n=D, T, Q, 5) for computing energetic (e.g., atomization energies, ionization energies, electron and proton affinities) and structural properties using the ab initio coupled cluster method including single, double, and quasiperturbative triple excitations [CCSD(T)] and the B3LYP density functional method was examined. The impact of relativistic corrections on these molecular properties was determined utilizing the Douglas-Kroll (cc-pVnZ-DK) and pseudopotential (cc-pVnZ-PP) forms of the correlation consistent basis sets. This work was extended to the characterization of molecular properties of novel chemically bonded krypton species, including HKrCl, FKrCF3, FKrSiF3, FKrGeF3, FKrCCF, and FKrCCKrF, and provided the first evidence of krypton bonding to germanium and the first di-krypton system. For second-row (Al-Ar) species, the construction of the core-valence correlation consistent basis sets, cc-pCVnZ was reexamined, and a revised series, cc-pCV(n+d)Z, was developed as a complement to the augmented tight-d valence series, cc-pV(n+d)Z. Benchmark calculations were performed to show the utility of these new sets for second-row species. Finally, the correlation consistent basis sets were used to study the structural and spectroscopic properties of Au(CO)Cl, providing conclusive evidence that luminescence in the solid-state can be attributed to oligomeric species rather than to the monomer.
5

Yao, Yuan. "Automated design of photonic quantum circuits." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAT005.

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L'informatique quantique est basée sur des phénomènes de physique quantique, tels que superposition et intrication et elle promet de révolutionner le monde de l'informatique. La photonique est une plateforme de premier plan pour réaliser l'informatique quantique tolérante aux erreurs. Elle possède plusieurs qualités : fonctionnement à température ambiante, fabricabilité à grande échelle à l'aide des fonderies existantes pour les puces de silicium et compatibilité avec les communications optique pour interconnecter différents ordinateurs quantiques.Notre objectif principal est d'automatiser la conception de circuits quantiques photoniques et de leurs interconnexions. Avant de pouvoir fabriquer un véritable ordinateur quantique photonique, il est essentiel de simuler numériquement et d'optimiser les circuits correspondants, qui sont en pratique construits à partir de composants gaussiens tels que des squeezers, des séparateurs de faisceaux, des déphaseurs et des détections homodynes. Pour atteindre l'universalité, nous avons également besoin d'effets non gaussiens, qui peuvent être fournis par des détecteurs résolvant le nombre de photons. Nous concevons des circuits à partir de cette boîte à outils et les optimisons pour diverses applications en utilisant divers algorithmes de descente de gradient, dont certains que nous avons adaptés à notre objectif.Les principaux apports sont :1. En photonique, les représentations de l'espace de Fock et de l'espace de phase sont des formalismes utiles pour décrire les états et les transformations quantiques. Nous introduisons une représentation unifiée dans l'espace de Fock de tous les objets gaussiens en termes d'une seule relation de récurrence linéaire qui peut générer de manière récursive leurs amplitudes dans l'espace de Fock.2. On retrouve la règle de composition des opérations gaussiennes dans l'espace de Fock, qui permet d'obtenir la bonne phase globale lors de la composition des opérations gaussiennes (normalement absente), et donc d'étendre notre modèle à des états qui s'écrivent comme combinaisons linéaires de gaussiennes.3. Notre représentation récursive est différentiable, permettant à calculer des gradients. Nous adaptons ensuite l'optimisation basée sur les gradients au problème d'optimisation des circuits. Nous implémentons un optimiseur Euclidien afin d'optimiser chaque composant. Ensuite, nous étudions deux manières de prendre en compte la géométrie: d'abord, nous appliquons l'optimisation Riemannienne, en combinant toutes les opérations gaussiennes en une transformation globale pour trouver ensuite la transformation optimisée, et la décomposer en composants optiques fondamentaux. Deuxièmement, nous généralisons une version complexe du gradient naturel pour les circuits afin d'accélérer le processus d'apprentissage.4. Nous donnons également quelques stratégies optimales basées sur les tâches pour utiliser nos relations de récurrence. De nouveaux algorithmes sont proposés pour calculer, par exemple, les amplitudes d'un état mixte et la matrice de transformation des interféromètres. De plus, nous dérivons un algorithme de contraction rapide pour les transformations gaussiennes, qui nous permet de "fusionner" le calcul des amplitudes d'une transformation gaussienne et son action sur n'importe quel état.5. Avec la simulation sur des circuits quantiques photoniques différentiables construits à partir de la relation de récurrence, nous pouvons concevoir automatiquement des circuits quantiques photoniques. Nous donnons la préparation de l'état comme premier exemple ; nous trouvons des circuits capables de produire des états de haute fidélité dans un temps raisonnable. Nous pouvons aussi optimiser un interféromètre à 216 modes pour rendre une expérience d'échantillonnage de boson gaussien difficile à usurper.6. Nous avons rendu ce travail accessible dans diverses bibliothèques open source: TheWalrus, StrawberryFields, Poenta et MrMustard
Quantum computing is based on quantum physics phenomena, such assuperposition and entanglement and it promises to revolutionize the world of computing. Photonics is a prominent platform for realizing fault-tolerant quantum computing. It has various qualities: working at room temperature, large-scale manufacturability using existing foundries for silicon chips, and compatibility with optical communication to interconnect different quantum computers.Our main goal is to automate the design of photonic quantum circuits and of their interconnects. Before a real photonic quantum computer can be manufactured, it is essential to numerically simulate and optimize the corresponding circuits, which in practice are built out of Gaussian components such as squeezers, beam-splitters, phase shifters, and homodyne detectors. To achieve universality, we also need non-Gaussian effects, which can be supplied by photon-number-resolving detectors. We design circuits from this toolbox and optimize them for various applications using various gradient descent algorithms, some of which we adapted to our purpose.The main contributions are:1. In photonics, Fock space and phase space representations are both useful formalisms to describe quantum states and transformations. We introduce a unified Fock space representation of all Gaussian objects in terms of a single linear recurrence relation that can recursively generate their Fock space amplitudes.2. We find the composition rule of Gaussian operations in Fock space, which allows us to obtain the correct global phase when composing Gaussian operations (normally absent from the phase space description), and therefore to extend our model to states that can be written as linear combinations of Gaussians.3. Our recursive representation is differentiable, allowing for a straightforward computation of the gradients of a Gaussian object with respect to any parametrization. We then adapt gradient-based optimization to the problem of circuit optimization. We implement a Euclidean optimizer (i.e. which doesn't take the geometry of parameter space unto account) in order to optimize each parametrized component of a circuit. Then we study two ways to account for geometry: first we apply Riemannian optimization, by combining all the Gaussian operations into a global transformation and following a geodesic on the manifold of symplectic matrices to find the optimized transformation, at which point we can decompose it back into fundamental optical components. Second, we generalize a complex version of the natural gradient for optical quantum circuits to accelerate the convergence of the training process.4. We also give some optimal task-based strategies for using our recurrence relations. New algorithms are proposed to calculate, for instance, the amplitudes of a mixed state and the transformation matrix of interferometers. In addition, we derive a fast contraction algorithm for Gaussian transformations, which allows us to "fuse" the computation of the amplitudes of a Gaussian transformation and its action on any state.5. With the simulation on differentiable photonic quantum circuits built from the recurrence relation, we can design photonic quantum circuits automatically. We give state preparation as the first example; we find circuits that can produce high-fidelity states in a reasonable time, such as cat states with mean photon number 4, fidelity 99.38%, and success probability 7.3%. We can also optimize a 216-mode interferometer to make a Gaussian Boson Sampling experiment harder to spoof.6. We made this work available in various open-source libraries: TheWalrus, StrawberryFields, Poenta, and MrMustard
6

Prascher, Brian P. Wilson Angela K. "Systematic approaches to predictive computational chemistry using the correlation consistent basis sets." [Denton, Tex.] : University of North Texas, 2009. http://digital.library.unt.edu/permalink/meta-dc-9920.

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Haruna, Luis Fernando. "Propriedades físicas de operações gaussianas sobre estados gaussianos emaranhados." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278360.

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Orientador: Marcos Cesar de Oliveira
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
Made available in DSpace on 2018-08-09T11:02:04Z (GMT). No. of bitstreams: 1 Haruna_LuisFernando_M.pdf: 1906903 bytes, checksum: 57f16fc8eb22ff66dcc420e1e340292f (MD5) Previous issue date: 2007
Resumo: Estudamos estados Gaussianos quânticos e as propriedades físicas associadas a operações sobre tal classe de estados que preservam a sua natureza Gaussiana. Propriedades gerais de matrizes de covariância globais representando estados Gaussianos bipartidos de dois modos podem ser decompostas em propriedades de matrizes de covariância locais e seus complementos de Schur. Demonstramos que dado um estado Gaussiano de dois modos r12 descrito por uma matriz de covariância V 4 × 4, o complemento de Schur de uma submatriz de covariância local V2 2 × 2 pode ser interpretado como uma nova matriz de covariância representando um operador Gaussiano do modo 1 condicionado a medições de paridade no modo 2. Como o valor médio da paridade está relacionado com a determinação da função de Wigner de um estado na origem do espaço de fase, que pode ser obtido facilmente através de experimentos de fotocontagem, este resultado nos permite estudar propriedades desta função em termos das probabilidades de medições pares e ímpares no modo local. Também generalizamos este procedimento para um estado Gaussiano de n modos e demonstramos que o operador dos n - 1 sistemas condicionado a projeções parciais de paridade está relacionado com uma matriz de covariância tal que seus elementos bloco 2 × 2 são complementos de Schur de matrizes especiais locais. A determinação da relação entre uma estrutura matemática (o complemento de Schur) com um processo físico permitiram a construção de um protocolo para a identificação de propriedades de emaranhamento de um estado Gaussiano de dois modos via apenas medições/operações locais e um canal de comunicação clássica entre as duas partes. Este protocolo se baseia na obtenção dos quatro invariantes simpléticos locais do grupo Sp(2, R) que determinam as propriedades de emaranhamento e de pureza do sistema Gaussiano de dois modos. Além disso, para uma classe de estados Gaussianos simétricos, que inclui por exemplo o estado comprimido com ruído térmico e o estado EPR, este protocolo também é útil para a reconstrução de sua matriz de covariância
Abstract: We study quantum Gaussian states and the physical properties associated to operations over such class of states, which preserve the respective Gaussian nature. General properties of global covariance matrices representing two-mode bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a two-mode Gaussian state r12 described by a 4 × 4 covariance matrix V, the Schur complement of a 2 × 2 local covariance sub-matrix V2 of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. As the parity mean value is related to the determination of the Wigner function of a state at the origin of the phase-space, which can be achieved straightforwardly by photocounting experiments, this result allow us to study properties of this function in terms of the odd and even measurements probabilities of the local mode. We also generalize this procedure to a n partite Gaussian state and we demonstrate that a n - 1 system operator conditioned to a partial projection is given by a covariance matrix such as its 2 × 2 block elements are Schur complements of special local matrices. The determination of the relation between a mathematical structure (the Schur complement) with a physical process allowed us to construct a protocol to identify the two-mode Gaussian state entanglement properties via only local measure-ments/ operations and a classical communication channel between the two parties. This protocol is established from the achievement of the four local sympletic invariants of the Sp(2, R) group, which determines the entanglement and purity properties of a two-mode Gaussian state. Moreover, for the symmetric Gaussian states class, which include for example the squeezed thermal state and the EPR state, this protocol is also uselfull for the covariance matrix reconstruction
Mestrado
Física
Mestre em Física
8

Monir, Md M. "A COMPUTATIONAL INVESTIGATION OF SECTORAL ZONING OF RARE EARTH ELEMENTS (REE) IN FLUORITE." Miami University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=miami1438881165.

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Prascher, Brian P. "Systematic Approaches to Predictive Computational Chemistry using the Correlation Consistent Basis Sets." Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc9920/.

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The development of the correlation consistent basis sets, cc-pVnZ (where n = D, T, Q, etc.) have allowed for the systematic elucidation of the intrinsic accuracy of ab initio quantum chemical methods. In density functional theory (DFT), where the cc-pVnZ basis sets are not necessarily optimal in their current form, the elucidation of the intrinsic accuracy of DFT methods cannot always be accomplished. This dissertation outlines investigations into the basis set requirements for DFT and how the intrinsic accuracy of DFT methods may be determined with a prescription involving recontraction of the cc-pVnZ basis sets for specific density functionals. Next, the development and benchmarks of a set of cc-pVnZ basis sets designed for the s-block atoms lithium, beryllium, sodium, and magnesium are presented. Computed atomic and molecular properties agree well with reliable experimental data, demonstrating the accuracy of these new s-block basis sets. In addition to the development of cc-pVnZ basis sets, the development of a new, efficient formulism of the correlation consistent Composite Approach (ccCA) using the resolution of the identity (RI) approximation is employed. The new formulism, denoted 'RI-ccCA,' has marked efficiency in terms of computational time and storage, compared with the ccCA formulism, without the introduction of significant error. Finally, this dissertation reports three separate investigations of the properties of FOOF-like, germanium arsenide, and silicon hydride/halide molecules using high accuracy ab initio methods and the cc-pVnZ basis sets.
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Sharkey, Keeper Layne. "Very Accurate Quantum Mechanical Non-Relativistic Spectra Calculations of Small Atoms & Molecules Employing All-Particle Explicitly Correlated Gaussian Basis Functions." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/560835.

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Due to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.
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Books on the topic "Gaussian quantum mechanics":

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Center, Ames Research, ed. Near Hartree-Fock quality Gaussian type orbital basis sets for the first- and third-row atoms. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1989.

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Center, Ames Research, ed. Near Hartree-Fock quality Gaussian type orbital basis sets for the first- and third-row atoms. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1989.

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Center, Ames Research, ed. Near Hartree-Fock quality Gaussian type orbital basis sets for the first- and third-row atoms. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1989.

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Knut, Faegri, and Ames Research Center, eds. High quality Gaussian basis sets for fourth-row atoms. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1992.

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Knut, Faegri, and Ames Research Center, eds. High quality Gaussian basis sets for fourth-row atoms. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1992.

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Bartók-Pártay, Albert. The Gaussian approximation potential: An interatomic potential derived from first principles quantum mechanics. Heidelberg: Springer, c2010., 2010.

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Dyall, Kenneth G. Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets. [Moffett Field, CA: NASA Ames Research Center, 1990.

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Poirier, Raymond. Handbook of Gaussian basis sets: A compendium for Ab-initio molecular orbital calculations. Amsterdam: Elsevier, 1985.

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Poirier, Raymond. Handbook of Gaussian basis sets: A compendium for ab-initio molecular orbital calculations. Amsterdam: Elsevier, 1985.

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Quinn, Charles M. Computational Quantum Chemistry: An Interactive Guide to Basis Set Theory. Academic Press, 2002.

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Book chapters on the topic "Gaussian quantum mechanics":

1

Miao, Haixing. "State Preparation: Non-Gaussian Quantum State." In Exploring Macroscopic Quantum Mechanics in Optomechanical Devices, 151–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25640-0_10.

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"A Gaussian integrals." In Quantum Mechanics, 455–64. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110751949-011.

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Zinn-Justin, Jean. "GAUSSIAN INTEGRALS." In Path Integrals in Quantum Mechanics, 1–26. Oxford University Press, 2004. http://dx.doi.org/10.1093/acprof:oso/9780198566748.003.0001.

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"A Mathematical Interlude: Gaussian Integrals." In Lectures on Quantum Mechanics, 467–78. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108555241.031.

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Anderson, Brian P. "Properties of 1D Gaussian Wavefunctions." In Field Guide to Quantum Mechanics. SPIE, 2019. http://dx.doi.org/10.1117/3.2512268.ap6.

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"Appendix C. The Gaussian Wave Packet Centered at k = k0." In Quantum Mechanics I, 433–36. Sciendo, 2018. http://dx.doi.org/10.2478/9783110627756-019.

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Kaiser, H., S. A. Werner, R. Clothier, H. Rauch, and H. Wölwitsch. "Quantum Interference of Non–Gaussian Wave Packets." In Foundations of Quantum Mechanics, 115–23. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814436687_0016.

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Zinn-Justin, Jean. "Gaussian integrals. Algebraic preliminaries." In Quantum Field Theory and Critical Phenomena, 1–17. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0001.

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Abstract:
In this work, the perturbative aspects of quantum mechanics (QM) and quantum field theory (QFT), to a large extent, are studied with functional (path or field) integrals and functional techniques. This physics textbook thus begins with a discussion of algebraic properties of Gaussian measures, and Gaussian expectation values for a finite number of variables. The important role of Gaussian measures is not unrelated to the central limit theorem of probabilities, although the interesting physics is generally hidden in essential deviations from Gaussian distributions. A few algebraic identities about Gaussian expectation values, in particular Wick's theorem are recalled. Integrals over some type of formally complex conjugate variables, directly relevant for boson systems are defined. Fermion systems require the introduction of Grassmann or exterior algebras, and the corresponding generalization of the notions of differentiation and integration. Both for complex and Grassmann integrals, Gaussian integrals, and Gaussian expectation values are calculated, and generalized Wick's theorems proven. The concepts of generating functions and Legendre transformation are recalled.
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Chen, Yanbei. "Quantum Optomechanics: from Gravitational Wave Detectors to Macroscopic Quantum Mechanics." In Quantum Optomechanics and Nanomechanics, 129–82. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198828143.003.0004.

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The quantum measurement process connects the quantum world and the classical world. The phrase ‘quantum measurement’ can have two meanings: measurement of a weak classical force, with the impact of quatum fluctuations on the measurement sensitivity, and the quantum mechanics of macroscopic objects: to try to prepare, manipulate and characterize the quantum state of a macroscopic quantum object through quantum measurement. Quantum noise leads to the Standard Quantum Limit (SQL), which provides the magnitude in which we must consider both measurement precision and measurement-induced back-action. The beginning of the chapter will be devoted to this thread of thought. The free-mass SQL actually provides a benchmark for the ‘quantum-ness’ of the system. We will show that a sub-SQL device can be used to prepare nearly pure quantum states and mechanical entanglement, as well as non-Gaussian quantum states that have no classical counterparts.
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Zinn-Justin, Jean. "Euclidean path integrals and quantum mechanics (QM)." In Quantum Field Theory and Critical Phenomena, 18–41. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0002.

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Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.

Conference papers on the topic "Gaussian quantum mechanics":

1

YALCIN, G. CIGDEM, YANI SKARLATOS, and K. GEDIZ AKDENIZ. "q-GAUSSIAN ANALYSIS IN COMPLEX POLYMERS." In Quantum Mechanics, Elementary Particles, Quantum Cosmology and Complexity. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814335614_0073.

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KHRENNIKOV, A. YU. "TO QUANTUM MECHANICS THROUGH GAUSSIAN INTEGRATION AND THE TAYLOR EXPANSION OF FUNCTIONALS OF CLASSICAL FIELDS." In Proceedings of the 26th Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770271_0027.

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A. JASIM, Nidaa. "THEORETICAL STUDY OF THE PHYSICAL PROPERTIES AND THERMODYNAMIC FUNCTIONS OF ASPIRIN USING QUANTUM MECHANICS CALCULATION (PARAMETRIC METHOD 3)." In VII. INTERNATIONAL SCIENTIFIC CONGRESSOF PURE,APPLIEDANDTECHNOLOGICAL SCIENCES. Rimar Academy, 2023. http://dx.doi.org/10.47832/minarcongress7-14.

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In this study, the theoretical quantum programs were relied upon to study some of the physical and radiodynamic properties, in addition to the spectral study of the aspirin compound. PM3 quantum chemistry methods and Gaussian 09 W program were applied to the calculation of the balanced dimentions (bond lengths, length angles in Angstrom) , The thermodynamic functions ( E0 , H0 ,A0 ,S0 ,CV ) was calculated of compounds studied and also some physical properties (EHOMO , ELUMO , ∆𝐸 , IP ) was also calculated. This study is important to reach additional theoretical information about acetylsalicylic acid (aspirin) using theoretical chemistry programs and compare it in the future with salicylic acid derivatives classified as analgesics to reach the best drugs on the other hand biological on the body.
4

Maignan, Aude, and Tony Scott. "Quantum Clustering Analysis: Minima of the Potential Energy Function." In 9th International Conference on Signal, Image Processing and Pattern Recognition (SPPR 2020). AIRCC Publishing Corporation, 2020. http://dx.doi.org/10.5121/csit.2020.101914.

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Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a 𝜎 value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size 𝜎, there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach “per block”. This technique decreases the number of particles (or samples) by approximating some groups of particles to weighted particles. These findings are not only useful to the quantum clustering problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics and other applications.
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Shafagh, Ida, Kevin J. Hughes, Mohamed Pourkashanian, and Alan Williams. "Investigation Into Bio-Aviation Reaction Mechanisms Using Quantum Mechanical Methods." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67512.

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Using high level model chemistries the C-C and C-H bond dissociation energies for methyl butanoate molecule (MB) were estimated using the Gaussian 03 program at the CBS-QB3 level of calculations. This consequently located the weaker bonds more likely to break. Thermal decomposition of MB over the temperatures 500 to 2000 K was theoretically studied and the rate constants for these channels were calculated. Crucial reactions in combustion, among which there are reactions of the fuel molecule with flame reactive radicals OH and CH3, were studied and the barrier heights for reactions including different hydrogen atoms transferring to the radicals were evaluated at the B3LYP/6-31+G(d, p) level of theory. The rate constants for these reactions are calculated over the temperatures 500 to 2000 K using the same level.
6

Frieden, B. Roy. "Fisher information and error complimentarity." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.fl3.

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The Cramer-Rao (CR) inequality e2I ≥ 1 represents complimentarity between (i) the size of mean-squares error e2 in estimation of a parameter θ from an observation y where y = θ + x, and (ii) the Fisher information I due to pdf p(x). In application to quantum mechanics, θ is the classical position of a particle, and I becomes the mean-squares momentum spread for the particle. Thus, the CR inequality becomes the Heisenberg uncertainty principle. The latter is, then, but one example of a general principle of error complimentarity. As applied to optical diffraction, θ is now the unknown centroid of a diffraction pattern. Here the CR inequality becomes e2z2 ≥ (λf/4π)2, where z2 is the mean-squares photon position in the lens pupil, λ is the light wavelength, and f is the focal length. Interestingly, here the uncertainty product can be made arbitrarily small. Another use is in the case of a nonideal gas kept at a constant temperature T. The gas is inside a container of unknown drift velocity θ. If p(x) defines the probability law on velocity x for particles of the gas, the CR inequality attains a minimum for the uncertainty product e2I when p(x) is Gaussian, i.e., when p(x) is a Boltzmann law. This describes the ideal gas scenario and gives it a new significance.
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Steely, S. L. "Harmonic oscillator fiducials for Hermite–Gaussian laser beams." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/oam.1993.thdd.46.

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This paper illustrates the similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite–Gaussian laser beams. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite–Gaussian laser beams.1
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Nurdin, Hendra I., Matthew R. James, and Ian R. Petersen. "Linear Quadratic Gaussian Control of Quantum Linear Stochastic Systems with Quantum Mechanical Controllers." In Quantum-Atom Optics Downunder. Washington, D.C.: OSA, 2007. http://dx.doi.org/10.1364/qao.2007.qme33.

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Vladimirov, Igor G. "A quantum mechanical version of price's theorem for Gaussian states." In 2014 4th Australian Control Conference (AUCC). IEEE, 2014. http://dx.doi.org/10.1109/aucc.2014.7358675.

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Gaeta, Z. Dacic, and C. R. Stroud. "Classical and quantum-mechanical dynamics of the quasiclassical state of the hydrogen atom." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.tue2.

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We study the dynamics of a circular-orbit wave packet1 and find that it has both classical and quantum features. A circular-orbit wave packet consists of aligned, standard hydrogenic eigenstates of maximum angular momentum (l = in = n − 1), superimposed with a Gaussian weighting function. We calculate the uncertainty products in all three degrees of freedom and find that, as the quantum numbers of the constituent eigenstates increase, the uncertainty products tend toward h/2. The classical aspect of the dynamics displays itself during revivals, when a well-localized wave packet travels along a Kepler orbit, obeying the classical equations of motion. Spreading and revivals (including fractional revivals2) of the wave packet, which are manifestations of its quantum nature, are related to the nonlinearity of the hydrogen atom Hamiltonian. We study fractional revivals of the wavepacket in detail.

Reports on the topic "Gaussian quantum mechanics":

1

Sawada, Shin-Ichi, Robert Heather, Bret Jackson, and Horia Metiu. The Strategy for Time Dependent Quantum Mechanical Calculations Using a Gaussian Wave Packet Representation of the Wave Function. Fort Belvoir, VA: Defense Technical Information Center, January 1985. http://dx.doi.org/10.21236/ada152709.

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