Academic literature on the topic 'Canonical and the associated perturbed quantum systems'
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Journal articles on the topic "Canonical and the associated perturbed quantum systems"
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CAVAGLIÀ, MARCO. "APPROXIMATE CANONICAL QUANTIZATION FOR COSMOLOGICAL MODELS." International Journal of Modern Physics D 08, no. 01 (February 1999): 101–15. http://dx.doi.org/10.1142/s0218271899000092.
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In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this in mind, we present a scheme for the (approximate) quantization of perturbed, nonintegrable, time-reparametrization invariant systems that uses (approximate) gauge invariant quantities. We apply the scheme to a couple of simple quantum cosmological models.
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Lupaşcu, A. I., and I. M. Popescu. "The time evolution of quantum systems with discrete energy spectra." Canadian Journal of Physics 64, no. 11 (November 1, 1986): 1546–50. http://dx.doi.org/10.1139/p86-275.
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Using the method of matrix functions, we describe the time evolution of quantum systems with discrete energy spectra. The time evolution of the state vectors and expressions for the perturbed eigenfunctions and their associated projectors are obtained for an atom with n discrete levels. The particular cases n = 2 and n = 3 are presented; level crossing and nonexponential decay of coupled states are emphasized.
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Kallush, Shimshon, Aviv Aroch, and Ronnie Kosloff. "Quantifying the Unitary Generation of Coherence from Thermal Quantum Systems." Entropy 21, no. 8 (August 19, 2019): 810. http://dx.doi.org/10.3390/e21080810.
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Coherence is associated with transient quantum states; in contrast, equilibrium thermal quantum systems have no coherence. We investigate the quantum control task of generating maximum coherence from an initial thermal state employing an external field. A completely controllable Hamiltonian is assumed allowing the generation of all possible unitary transformations. Optimizing the unitary control to achieve maximum coherence leads to a micro-canonical energy distribution on the diagonal energy representation. We demonstrate such a control scenario starting from a given Hamiltonian applying an external field, reaching the control target. Such an optimization task is found to be trap-less. By constraining the amount of energy invested by the control, maximum coherence leads to a canonical energy population distribution. When the optimization procedure constrains the final energy too tightly, local suboptimal traps are found. The global optimum is obtained when a small Lagrange multiplier is employed to constrain the final energy. Finally, we explore the task of generating coherences restricted to be close to the diagonal of the density matrix in the energy representation.
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Bruce, S. A., and J. F. Diaz-Valdes. "Generalized Electromagnetic Fields Associated with the Hydrogen-Like Atom Problem." Zeitschrift für Naturforschung A 74, no. 1 (December 19, 2018): 43–50. http://dx.doi.org/10.1515/zna-2018-0372.
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AbstractIt is known that the principle of minimal coupling in quantum mechanics determines a unique interaction form for a charged particle. By properly redefining the canonical commutation relation between (canonical) conjugate components of position and momentum of the particle, e.g. an electron, we restate the Dirac equation for the hydrogen-like atom problem incorporating a generalized minimal electromagnetic coupling. The corresponding interaction keeps the $1/\left|\mathbf{q}\right|$ dependence in both the scalar potential $V\left({\left|\mathbf{q}\right|}\right)$ and the vector potential $\mathbf{A}\left(\mathbf{q}\right)$ ($\left|{\mathbf{A}\left(\mathbf{q}\right)}\right|\sim 1/\left|\mathbf{q}\right|$). This problem turns out to be exactly solvable; moreover, the eigenstates and eigenvalues can be obtained in an elementary fashion. Some feasible models within this approach are discussed. Then we make a few remarks about the breaking of supersymmetry. Finally, we briefly comment on the possible Lie algebra (dynamical symmetry algebra) of these relativistic quantum systems.
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Sergi, Alessandro, Gabriel Hanna, Roberto Grimaudo, and Antonino Messina. "Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths." Symmetry 10, no. 10 (October 16, 2018): 518. http://dx.doi.org/10.3390/sym10100518.
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Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.
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ALDAYA, V., M. CALIXTO, J. GUERRERO, and F. F. LÓPEZ-RUIZ. "SYMMETRIES OF NON-LINEAR SYSTEMS: GROUP APPROACH TO THEIR QUANTIZATION." International Journal of Geometric Methods in Modern Physics 08, no. 06 (September 2011): 1329–54. http://dx.doi.org/10.1142/s0219887811005713.
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We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically non-perturbative, is primarily intended for non-linear systems, although needless to say that finding the basic symmetry associated with a given (quantum) physical problem is in general a difficult task, which many times nearly emulates the complexity of finding the actual (classical) solutions. Apart from some interesting examples related to the electromagnetic and gravitational particle interactions, where an algebraic version of the Equivalence Principle naturally arises, we attempt to the quantum description of non-linear sigma models. In particular, we present the actual quantization of the partial-trace non-linear SU (2) sigma model as a representative case of non-linear quantum field theory.
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Izquierdo, Zoe Gonzalez, Itay Hen, and Tameem Albash. "Testing a Quantum Annealer as a Quantum Thermal Sampler." ACM Transactions on Quantum Computing 2, no. 2 (July 2021): 1–20. http://dx.doi.org/10.1145/3464456.
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Motivated by recent experiments in which specific thermal properties of complex many-body systems were successfully reproduced on a commercially available quantum annealer, we examine the extent to which quantum annealing hardware can reliably sample from the thermal state in a specific basis associated with a target quantum Hamiltonian. We address this question by studying the diagonal thermal properties of the canonical one-dimensional transverse-field Ising model on a D-Wave 2000Q quantum annealing processor. We find that the quantum processor fails to produce the correct expectation values predicted by Quantum Monte Carlo. Comparing to master equation simulations, we find that this discrepancy is best explained by how the measurements at finite transverse fields are enacted on the device. Specifically, measurements at finite transverse field require the system to be quenched from the target Hamiltonian to a Hamiltonian with negligible transverse field, and this quench is too slow. The limitations imposed by such hardware make it an unlikely candidate for thermal sampling, and it remains an open question what thermal expectation values can be robustly estimated in general for arbitrary quantum many-body systems.
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ALBEVERIO, SERGIO, HANNO GOTTSCHALK, and MINORU W. YOSHIDA. "SYSTEMS OF CLASSICAL PARTICLES IN THE GRAND CANONICAL ENSEMBLE, SCALING LIMITS AND QUANTUM FIELD THEORY." Reviews in Mathematical Physics 17, no. 02 (March 2005): 175–226. http://dx.doi.org/10.1142/s0129055x05002327.
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Euclidean quantum fields obtained as solutions of stochastic partial pseudo differential equations driven by a Poisson white noise have paths given by locally integrable functions. This makes it possible to define a class of ultra-violet finite local interactions for these models (in any space-time dimension). The corresponding interacting Euclidean quantum fields can be identified with systems of classical "charged" particles in the grand canonical ensemble with an interaction given by a nonlinear energy density of the "static field" generated by the particles' charges via a "generalized Poisson equation". A new definition of some well-known systems of statistical mechanics is given by formulating the related field theoretic local interactions. The infinite volume limit of such systems is discussed for models with trigonometric interactions using a representation of such models as Widom–Rowlinson models associated with (formal) Potts models at imaginary temperature. The infinite volume correlation functional of such Potts models can be constructed by a cluster expansion. This leads to the construction of extremal Gibbs measures with trigonometric interactions in the low-density high-temperature (LD-HT) regime. For Poissonian models with certain trigonometric interactions an extension of the well-known relation between the (massive) sine-Gordon model and the Yukawa particle gas connecting characteristic and correlation functionals is given and used to derive infinite volume measures for interacting Poisson quantum field models through an alternative route. The continuum limit of the particle systems under consideration is also investigated and the formal analogy with the scaling limit of renormalization group theory is pointed out. In some simple cases the question of (non-) triviality of the continuum limits is clarified.
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Ballesteros, Angel, Flaminia Giacomini, and Giulia Gubitosi. "The group structure of dynamical transformations between quantum reference frames." Quantum 5 (June 8, 2021): 470. http://dx.doi.org/10.22331/q-2021-06-08-470.
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Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference frames. This led to a relational description of the phase space variables of the quantum system of which the quantum reference frames are part of. While such transformations were shown to be symmetries of the system's Hamiltonian, the question remained unanswered as to whether they enjoy a group structure, similar to that of the Galilei group relating classical reference frames in quantum mechanics. In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. We further find that the elements of this new algebra are in fact the building blocks of the quantum reference frames transformations previously identified, which we recover. Finally, we show how the transformations between classical reference frames described by the standard Galilei group symmetries can be obtained from the group of transformations between quantum reference frames by taking the zero limit of the parameter that governs the additional noncommutativity introduced by the quantum nature of inertial transformations.
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CASTELLANA, MICHELE, and GIOVANNI MONTANI. "BRST SYMMETRY TOWARDS THE GAUSS CONSTRAINT FOR GENERAL RELATIVITY." International Journal of Modern Physics A 23, no. 08 (March 30, 2008): 1218–21. http://dx.doi.org/10.1142/s0217751x08040093.
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Quantization of systems with constraints can be carried on with several methods. In the Dirac's formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, differently from the Dirac's method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. The condition we gain differs form the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge fixing functionals. We finally discuss how it should be possible to obtain all the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach.
Dissertations / Theses on the topic "Canonical and the associated perturbed quantum systems"
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Ahmed, Istiaque, and s3119889@student rmit edu au. "Canonical and Perturbed Quantum Potential-Well Problems: A Universal Function Approach." RMIT University. Electrical and Computer Engineering, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080108.124715.
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The limits of the current micro-scale electronics technology have been approaching rapidly. At nano-scale, however, the physical phenomena involved are fundamentally different than in micro-scale. Classical and semi-classical physical principles are no longer powerful enough or even valid to describe the phenomena involved. The rich and powerful concepts in quantum mechanics have become indispensable. There are several commercial software packages already available for modeling and simulation of the electrical, magnetic, and mechanical characteristics and properties of the nano-scale devices. However, our objective here is to go one step further and create a physics-based problem-adapted solution methodology. We carry out computation for eigenfunctions of canonical and the associated perturbed quantum systems and utilize them as co-ordinate functions for solving more complex problems. We have profoundly worked with the infinite quantum potential-well problem, since they have closed-form solutions and therefore are analytically known eigenfunctions. Perturbation of the infinite quantum potential-well was done through a single box function, multiple box functions, and with a triangular function. The proposed solution concept utilizes the notion of
Book chapters on the topic "Canonical and the associated perturbed quantum systems"
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Zinn-Justin, Jean. "Quantum statistical physics: Functional integration formalism." In Quantum Field Theory and Critical Phenomena, 64–89. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0004.
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The functional integral representation of the density matrix at thermal equilibrium in non-relativistic quantum mechanics (QM) with many degrees of freedom, in the grand canonical formulation is introduced. In QM, Hamiltonians H(p,q) can be also expressed in terms of creation and annihilation operators, a method adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism, quantum operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables that correspond in the classical limit to a complex parametrization of phase space. The formalism is adapted to the description of many-body boson systems. To this formalism corresponds a path integral representation of the density matrix at thermal equilibrium, where paths belong to complex spaces, instead of the more usual position–momentum phase space. A parallel formalism can be set up to describe systems with many fermion degrees of freedom, with Grassmann variables replacing complex variables. Both formalisms can be generalized to quantum gases of Bose and Fermi particles in the grand canonical formulation. Field integral representations of the corresponding quantum partition functions are derived.