Готові списки джерел за темами / Quantum mixed spin

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Добірка наукової літератури з теми "Quantum mixed spin"

Автор: Grafiati

Опубліковано: 10 березня 2023

Оновлено: 11 березня 2023

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Статті в журналах з теми "Quantum mixed spin"

Geiger, Davi, and Zvi M. Kedem. "Spin Entropy." Entropy 24, no. 9 (September 14, 2022): 1292. http://dx.doi.org/10.3390/e24091292.

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Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states.

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Takano, Ken'ichi. "Disordered Phases in Mixed Quantum Spin Chains." Progress of Theoretical Physics Supplement 145 (2002): 170–75. http://dx.doi.org/10.1143/ptps.145.170.

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Zhang, Pan-Pan, Jie Wang, Yu-Liang Xu, Chun-Yang Wang, and Xiang-Mu Kong. "Quantum Entanglements in mixed-spin XY systems." Physica A: Statistical Mechanics and its Applications 566 (March 2021): 125643. http://dx.doi.org/10.1016/j.physa.2020.125643.

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Hao, Xiang, and Shiqun Zhu. "Entanglement in a quantum mixed-spin chain." Physics Letters A 366, no. 3 (June 2007): 206–10. http://dx.doi.org/10.1016/j.physleta.2007.01.053.

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Li, Junyao, Xiaofeng Liu, Lingyun Wan, Xinming Qin, Wei Hu, and Jinlong Yang. "Mixed magnetic edge states in graphene quantum dots." Multifunctional Materials 5, no. 1 (January 10, 2022): 014001. http://dx.doi.org/10.1088/2399-7532/ac44fe.

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Abstract Graphene quantum dots (GQDs) exhibit abundant magnetic edge states with promising applications in spintronics. Hexagonal zigzag GQDs possess a ground state with an antiferromagnetic (AFM) inter-edge coupling, followed by a metastable state with ferromagnetic (FM) inter-edge coupling. By analyzing the Hubbard model and performing large-scale spin-polarized density functional theory calculations containing thousands of atoms, we predict a series of new mixed magnetic edge states of GQDs arising from the size effect, namely mix-n, where n is the number of spin arrangement parts at each edge, with parallel spin in the same part and anti-parallel spin between adjacent parts. In particular, we demonstrate that the mix-2 state of bare GQDs (C 6 N 2 ) appears when N ⩾ 4 and the mix-3 state appears when N ⩾ 6 , where N is the number of six-membered-ring at each edge, while the mix-2 and mix-3 magnetic states appear in the hydrogenated GQDs with N = 13 and N = 15, respectively.

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FAN, HONGWEI, ZHAOXIN XU, and HEPING YING. "QUANTUM MONTE CARLO STUDY ON RANDOM BOND MIXED-SPIN CHAIN." International Journal of Modern Physics B 21, no. 23n24 (September 30, 2007): 4196–200. http://dx.doi.org/10.1142/s0217979207045402.

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The effects of bond randomness on the quantum mixed-spin chain 1-1-1/2-1/2 are investigated by a quantum Monte Carlo study. We find that around the critical point of original pure system, quantum Griffiths phases appears, and its region is enlarged with increasing of bond randomness. Moreover, the critical behavior of the original quantum critical point has been changed by the randomness.

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Batle, J., M. Abutalib, S. Abdalla, and Ahmed Farouk. "Revival of Bell nonlocality across a quantum spin chain." International Journal of Quantum Information 14, no. 07 (October 2016): 1650037. http://dx.doi.org/10.1142/s0219749916500374.

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The transmission of pure and mixed states along a quantum spin chain is investigated. Nonlocality between two qubits will evolve as it is transmitted through the quantum channel in a way that may violate or not the Clauser–Horne–Shimony–Holt (CHSH) Bell inequality at different times. This violation of local realism is analogue to the so-called sudden death and sudden birth features of entanglement. In the quantum channel, which will turn to be a damping one, some (mixed) states will be preferred according to the nature of the quantum correlations that are preserved during the evolution along the spin chain.

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Brieskorn, G., and K. D. Usadel. "Quantum spin glasses with randomly mixed uniaxial anisotropies." Journal of Physics C: Solid State Physics 19, no. 18 (June 30, 1986): 3413–20. http://dx.doi.org/10.1088/0022-3719/19/18/013.

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Wang, Jin Tong, Aaron X. Kan, and J. D. Fan. "The origin of the spooky behavior of quantum particles: Time reversal." Modern Physics Letters A 34, no. 25 (August 20, 2019): 1950199. http://dx.doi.org/10.1142/s0217732319501992.

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In this paper, we study the origin of the quantum particle entanglement. Particles will have one mixed wave function as soon as they are created, which are called quantum particle entanglement. Electron spin states are used as an example to discuss this topic. When two electrons are created simultaneously, they have two different mixed quantum spin states. Before the measurement of its spin, we cannot determine its spin state. However, as soon as the spin of one of the electrons is determined (measured), the spin of the other will definitely be in the opposite state, regardless of how far they are away from each other. This paper uses the mechanism that the wave packet spreads as soon as they are created and then the wave packet shrinks when it undergoes a measurement to interpret this spooky phenomenon mentioned above.

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Sakai, T., T. Tonegawa, and K. Okamoto. "Quantum magnetization plateau of an anisotropic mixed spin chain." Journal of Physics: Conference Series 51 (November 1, 2006): 163–66. http://dx.doi.org/10.1088/1742-6596/51/1/037.

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Більше джерел

Дисертації з теми "Quantum mixed spin"

Bischof, Rainer. "Gaussian Critical Line in Anisotropic Mixed Quantum Spin Chains." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-107225.

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By numerical methods, two models of anisotropic mixed quantum spin chains, consisting of spins of two different sizes, Sa = 1/2 and Sb = 1 as well as Sb = 3/2, are studied with respect to their critical properties at quantum phase transitions in a selected region of parameter space. The quantum spin chains are made up of basecells of four spins, according to the structure Sa − Sa − Sb − Sb. They are described by the XXZ Hamiltonian, that extends the quantum Heisenberg model by a variable anisotropic exchange interaction. As additional control parameter, an alternating exchange constant between nearest-neighbour spins is introduced. Insight gained by complementary application of exact diagonalization and quantum Monte Carlo simulations, as well as appropriate methods of analysis, is embedded in the broad existing knowledge on homogeneous quantum spin chains. In anisotropic homogeneous quantum spin chains, there exist phase boundaries with continuously varying critical exponents, the Gaussian critical lines, along which, in addition to standard scaling relations, further extended scaling relations hold. Reweighting methods, also applied to improved quantum Monte Carlo estimators, and finite-size scaling analysis of simulation data deliver a wealth of numerical results confirming the existence of a Gaussian critical line also in the mixed spin models considered. Extrapolation of exact data offers, apart from confirmation of simulation data, furthermore, insight into the conformal operator content of the model with Sb = 1
Mittels numerischer Methoden werden zwei Modelle anisotroper gemischter Quantenspinketten, bestehend aus Spins zweier unterschiedlicher Größen, Sa = 1/2 und Sb = 1 sowie Sb = 3/2, hinsichtlich ihrer kritischen Eigenschaften an Quanten-Phasenübergängen in einem ausgewählten Parameterbereich untersucht. Die Quantenspinketten sind aus Basiszellen zu vier Spins, gemäß der Struktur Sa − Sa − Sb − Sb, aufgebaut. Sie werden durch den XXZ Hamiltonoperator beschrieben, der das isotrope Quanten-Heisenberg Modell um eine variable anistrope Austauschwechselwirkung erweitert. Als zusätzlicher Kontrollparameter wird eine alterniernde Kopplungskonstante zwischen unmittelbar benachbarten Spins eingeführt. Die durch komplementäre Anwendung exakter Diagonalisierung und Quanten-Monte-Carlo Simulationen, sowie entsprechender Analyseverfahren, gewonnenen Erkenntnisse werden in das umfangreiche existierende Wissen über homogene Quantenspinketten eingebettet. Im Speziellen treten in anisotropen homogenen Quantenspinketten Phasengrenzen mit kontinuierlich variierenden kritischen Exponenten auf, die Gaußschen kritischen Linien, auf denen neben den herkömmlichen auch erweiterte Skalenrelationen Gültigkeit besitzen. Umgewichtungsmethoden, speziell auch angewandt auf verbesserte Quanten-Monte-Carlo Schätzer, und Endlichkeitsskalenanalyse von Simulationsdaten liefern eine Fülle von numerischen Ergebnissen, die das Auftreten der Gaußschen kritischen Linie auch in den untersuchten gemischten Quantenspinketten bestätigen. Die Extrapolation exakter Daten bietet, neben der Bestätigung der Simulationsdaten, darüber hinaus Einblick in einen Teil des konformen Operatorinhalts des Modells mit Sb = 1

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Bischof, Rainer [Verfasser], Wolfhard [Akademischer Betreuer] Janke, Wolfhard [Gutachter] Janke, and Matthias [Gutachter] Vojta. "Gaussian Critical Line in Anisotropic Mixed Quantum Spin Chains / Rainer Bischof ; Gutachter: Wolfhard Janke, Matthias Vojta ; Betreuer: Wolfhard Janke." Leipzig : Universitätsbibliothek Leipzig, 2013. http://d-nb.info/1238366007/34.

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Vieira, Andre de Pinho. "Efeitos de desordem ou aperiodicidade sobre o comportamento de sistemas magnéticos." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-23022012-155648/.

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Consideramos os efeitos de desordem ou aperiodicidade sobre três sistemas magnéticos distintos. Inicialmente, apresentamos um modelo fenomenológico para descrever a dependência térmica da magnetização remanente induzida por diluição numa classe de antiferromagnetos quase-unidimensionais. O modelo trata exatamente as correlações ao longo da direção dominante, levando em conta as demais interações por meio de um campo efetivo. Em seguida, utilizamos uma aproximação autoconsistente de Bethe-Peierls para avaliar os efeitos de um campo cristalino aleatório sobre os diagramas de fases de um modelo de Ising de spins mistos. Mostramos que a desordem é capaz de modificar a natureza dos pontos multicríticos existentes no limite uniforme do modelo. Finalmente, estudamos os efeitos de interações aleatórias ou aperiódicas sobre o comportamento da cadeia XX quântica em baixas temperaturas, através de câlculos numéricos baseados no mapeamento do sistema em um modelo de férmions livres. Apontamos evidências de que, em temperatura zero, existe um único ponto fixo universal, característico de uma fase de singleto aleatório, que governa o comportamento do modelo na presença de interações desordenadas. No caso de interações aperiódicas,obtemos resultados consistentes com previsões de grupo de renormalização, indicando, para uma certa classe de seqüências de substituição, um comportamento semelhante àquele associado à desordem.
We consider effects of disorder or aperiodicity on three different magnetic systems. First, we present a phenomenological model to describe the thermal dependence of the dilution-induced remanent magnetization in a class of quasi-one-dimensional antiferromagnets. The model treats correlations along the dominant direction in an exact way, while including the remaining inte-. i ractions via an effective field. Then, we use a self-consistent Bethe-Peierls ~ j .. approximation to gauge the effects of a random crystal field on the phase diagram of a mixed-spin Ising mode!. We show that disorder may have profound effects on the multicritical behavior associated with the uniform limit of the mo de!. Finally, we study effects of random or aperiodic interactions on the behavior of the quantum XX chain at low temperatures, by performing numerical calculations based on a mapping of the system onto a free-fermion mo de!. . We present evidence that, at zero temperature, there exists a single, universal fixed-point, associated with a random-singlet phase, which governs the behavior of the model in the presence of disordered interactions. In the case of aperiodic interactions, our results are consistent with renormalizationgroup predictions, indicating, for a certain class of substitution sequences, a behavior similar to the one induced by disorder.

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Bischof, Rainer. "Gaussian Critical Line in Anisotropic Mixed Quantum Spin Chains." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A11852.

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Анотація:

By numerical methods, two models of anisotropic mixed quantum spin chains, consisting of spins of two different sizes, Sa = 1/2 and Sb = 1 as well as Sb = 3/2, are studied with respect to their critical properties at quantum phase transitions in a selected region of parameter space. The quantum spin chains are made up of basecells of four spins, according to the structure Sa − Sa − Sb − Sb. They are described by the XXZ Hamiltonian, that extends the quantum Heisenberg model by a variable anisotropic exchange interaction. As additional control parameter, an alternating exchange constant between nearest-neighbour spins is introduced. Insight gained by complementary application of exact diagonalization and quantum Monte Carlo simulations, as well as appropriate methods of analysis, is embedded in the broad existing knowledge on homogeneous quantum spin chains. In anisotropic homogeneous quantum spin chains, there exist phase boundaries with continuously varying critical exponents, the Gaussian critical lines, along which, in addition to standard scaling relations, further extended scaling relations hold. Reweighting methods, also applied to improved quantum Monte Carlo estimators, and finite-size scaling analysis of simulation data deliver a wealth of numerical results confirming the existence of a Gaussian critical line also in the mixed spin models considered. Extrapolation of exact data offers, apart from confirmation of simulation data, furthermore, insight into the conformal operator content of the model with Sb = 1.
Mittels numerischer Methoden werden zwei Modelle anisotroper gemischter Quantenspinketten, bestehend aus Spins zweier unterschiedlicher Größen, Sa = 1/2 und Sb = 1 sowie Sb = 3/2, hinsichtlich ihrer kritischen Eigenschaften an Quanten-Phasenübergängen in einem ausgewählten Parameterbereich untersucht. Die Quantenspinketten sind aus Basiszellen zu vier Spins, gemäß der Struktur Sa − Sa − Sb − Sb, aufgebaut. Sie werden durch den XXZ Hamiltonoperator beschrieben, der das isotrope Quanten-Heisenberg Modell um eine variable anistrope Austauschwechselwirkung erweitert. Als zusätzlicher Kontrollparameter wird eine alterniernde Kopplungskonstante zwischen unmittelbar benachbarten Spins eingeführt. Die durch komplementäre Anwendung exakter Diagonalisierung und Quanten-Monte-Carlo Simulationen, sowie entsprechender Analyseverfahren, gewonnenen Erkenntnisse werden in das umfangreiche existierende Wissen über homogene Quantenspinketten eingebettet. Im Speziellen treten in anisotropen homogenen Quantenspinketten Phasengrenzen mit kontinuierlich variierenden kritischen Exponenten auf, die Gaußschen kritischen Linien, auf denen neben den herkömmlichen auch erweiterte Skalenrelationen Gültigkeit besitzen. Umgewichtungsmethoden, speziell auch angewandt auf verbesserte Quanten-Monte-Carlo Schätzer, und Endlichkeitsskalenanalyse von Simulationsdaten liefern eine Fülle von numerischen Ergebnissen, die das Auftreten der Gaußschen kritischen Linie auch in den untersuchten gemischten Quantenspinketten bestätigen. Die Extrapolation exakter Daten bietet, neben der Bestätigung der Simulationsdaten, darüber hinaus Einblick in einen Teil des konformen Operatorinhalts des Modells mit Sb = 1.

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Milazzo, Lisa. "How resonance Raman spectroscopy can give valuable insights into diverse aspects of heme protein structure and function." Doctoral thesis, 2019. http://hdl.handle.net/2158/1154362.

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Resonance Raman (RR) spectroscopy complemented by UV-Vis absorption spectroscopy is a very powerful technique to investigate the structure-function relationships of heme proteins, a widely distributed and biological relevant class of proteins which can play different biological functions. Since the protein activity is tightly linked to the structure of the heme active site, my study has been devoted to the investigation of several heme proteins involved in important biological processes, to obtain a comprehensive spectroscopic signature, with the aim to highlight the relationship between the heme pocket architecture and the protein function. The studies were carried out on native proteins and selected site-directed mutants, at both room (298 K) and low (80 K) temperature, at various pH, and in presence of various exogenous ligands, spanning the excitation wavelengths from UV to the visible region.

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Книги з теми "Quantum mixed spin"

Launay, Jean-Pierre, and Michel Verdaguer. Electrons in Molecules. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198814597.001.0001.

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The book treats in a unified way electronic properties of molecules (magnetic, electrical, photophysical), culminating with the mastering of electrons, i.e. molecular electronics and spintronics and molecular machines. Chapter 1 recalls basic concepts. Chapter 2 describes the magnetic properties due to localized electrons. This includes phenomena such as spin cross-over, exchange interaction from dihydrogen to extended molecular magnetic systems, and magnetic anisotropy with single-molecule magnets. Chapter 3 is devoted to the electrical properties due to moving electrons. One considers first electron transfer in discrete molecular systems, in particular in mixed valence compounds. Then, extended molecular solids, in particular molecular conductors, are described by band theory. Special attention is paid to structural distortions (Peierls instability) and interelectronic repulsions in narrow-band systems. Chapter 4 treats photophysical properties, mainly electron transfer in the excited state and its applications to photodiodes, organic light emitting diodes, photovoltaic cells and water photolysis. Energy transfer is also treated. Photomagnetism (how a photonic excitation modifies magnetic properties) is introduced. Finally, Chapter 5 combines the previous knowledge for three advanced subjects: first molecular electronics in its hybrid form (molecules connected to electrodes acting as wires, diodes, memory elements, field-effect transistors) or in the quantum computation approach. Then, molecular spintronics, using, besides the charge, the spin of the electron. Finally the theme of molecular machines is presented, with the problem of the directionality control of their motion.

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Частини книг з теми "Quantum mixed spin"

Indiani, Chiara, Barry D. Howes, Alessandro Feis, and Giulietta Smulevich. "Calcium depletion of horseradish peroxidase generates a quantum mechanical mixed-spin heme state." In Spectroscopy of Biological Molecules: New Directions, 145–46. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4479-7_62.

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Xia, Jian-Bai, and Duan-Yang Liu. "Spin Polarization of a Rashba Electron with a Mixed State." In Quantum Waveguide in Microcircuits, edited by Wei-Dong Sheng, 355–65. Jenny Stanford Publishing, 2017. http://dx.doi.org/10.1201/9781315364773-16.

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"Density Operators and Matrices." In Essential Mathematics for NMR and MRI Spectroscopists, 510–60. The Royal Society of Chemistry, 2016. http://dx.doi.org/10.1039/bk9781782627975-00510.

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The density matrix is a very convenient way to do calculations for a large number of spin systems and is developed from the fundamental ideas of quantum mechanics. The idea of pure and mixed states is introduced and used to develop an expression for the single-spin density matrix as it applies to NMR spectroscopy. Multiple-spin density matrices are produced by using the outer product of single-spin matrices and their commutation properties are examined. A very useful form of the scalar coupling density operator is developed and used, along with the chemical shift operator, to calculate the spectrum of a weakly coupled two-spin system. The density operator of spin-1 is explored. Density matrix calculations in perturbed systems are investigated in preparation for relaxation calculations. Strong coupling is discussed and compared to the weak coupling approximation, using the full scalar coupling Hamiltonian and matrix diagonalisation techniques.

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G. Kaplan, Ilya. "Modern State of the Conventional DFT Method Studies and the Limits Following from the Quantum State of the System and Its Total Spin." In Density Functional Theory - Recent Advances, New Perspectives and Applications [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.102670.

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At present, the density functional theory (DFT) approach became the most widely used method for study molecules and solids. In the atmosphere of such great popularity, it is particularly important to know the limits of the applicability of DFT methods. In this chapter, I will discuss the modern state of DFT studies basing on the last publications and will consider in detail two cases when the conventional DFT approaches, in which used only electron density and its modifications by gradients, cannot be applied. First, the case related to the total spin S of the state. As I rigorously proved for an arbitrary N-electron state by group theoretical methods, the electron density does not depend on the total spin S of the state. From this follows that the Kohn-Sham equations have the same form for states with different S. The critical survey of elaborated DFT procedures, in which the spin is taken into account, shows that they modified only exchange functionals, and the correlation functionals do not correspond to the spin of the state. The point is that the conception of spin in principle cannot be defined in the framework of the electron density formalism, and this is the main reason of the problems arising in the study by DFT approaches the magnetic properties of the transition metals. The possible way of resolving spin problems can be found in the two-particle reduced density matrix formulation of DFT. In the end, it will be considered the case of the degenerated states, in which, as follows from the adiabatic approximation, the electron density may not be defined, since electronic and nuclear motions cannot be separated, since, the vibronic interaction mixed them.

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Тези доповідей конференцій з теми "Quantum mixed spin"

BISCHOF, R., and W. JANKE. "CRITICAL EXPONENTS OF MIXED QUANTUM SPIN CHAIN." In Proceedings of the 9th International Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812837271_0075.

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Adhikari, Satyabrata, A. S. Majumdar, D. Home, A. K. Pan, Dipankar Home, Guruprasad Kar, and Archan S. Majumda. "Swapping path-spin intraparticle entanglement onto spin-spin mixed interparticle entanglement involving amplitude damping channel." In 75 YEARS OF QUANTUM ENTANGLEMENT: FOUNDATIONS AND INFORMATION THEORETIC APPLICATIONS: S. N. Bose National Centre for Basic Sciences Silver Jubilee Symposium. AIP, 2011. http://dx.doi.org/10.1063/1.3635851.

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Vengrenovich, R. D., A. V. Moskalyuk, and S. V. Yarema. "Formation of quantum dots in heterostructures in mixed diffusion conditions." In SPIE Proceedings, edited by Oleg V. Angelsky. SPIE, 2006. http://dx.doi.org/10.1117/12.679935.

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Wright, John, Carolyn Auchter, Chen-Kuan Chou, Richard D. Graham, Thomas W. Noel, Tomasz Sakrejda, Zichao Zhou, and Boris B. Blinov. "Scalable quantum computing architecture with mixed species ion chains." In SPIE Sensing Technology + Applications, edited by Eric Donkor, Andrew R. Pirich, and Michael Hayduk. SPIE, 2015. http://dx.doi.org/10.1117/12.2177997.

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O'Leary, Shannon, Hailin Wang та John Prineas. "A Λ-type system for electron spins in a mixed-type GaAs/AlAs quantum qell". У 2006 Conference on Lasers & Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS). IEEE, 2006. http://dx.doi.org/10.1109/cleo.2006.4628992.

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Lin, Y. C., W. C. Chou, A. S. Susha, and A. L. Rogach. "Förster resonance energy transfer in mixed-size CdTe quantum dots with optimized donor-acceptor concentration ratio." In SPIE OPTO, edited by Kong-Thon Tsen, Jin-Joo Song, Markus Betz, and Abdulhakem Y. Elezzabi. SPIE, 2011. http://dx.doi.org/10.1117/12.875859.

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Hübers, H. W., S. G. Pavlov, H. Richter, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, and D. A. Ritchie. "Heterodyne receiver at 2.5 THz with quantum cascade laser and hot electron bolometric mixer." In SPIE Astronomical Telescopes + Instrumentation, edited by Jonas Zmuidzinas, Wayne S. Holland, Stafford Withington, and William D. Duncan. SPIE, 2006. http://dx.doi.org/10.1117/12.671395.

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Richter, H., A. D. Semenov, S. G. Pavlov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, et al. "Development of a THz heterodyne receiver with quantum cascade laser and hot electron bolometer mixer for standoff detection of explosive material." In SPIE Defense, Security, and Sensing, edited by Mehdi Anwar, Nibir K. Dhar, and Thomas W. Crowe. SPIE, 2009. http://dx.doi.org/10.1117/12.818134.

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