Relevant bibliographies by topics / Non-markovian stochastic Schrodinger equations

Academic literature on the topic 'Non-markovian stochastic Schrodinger equations'

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Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Non-markovian stochastic Schrodinger equations"

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Vanchurin, Vitaly. "Towards a Theory of Quantum Gravity from Neural Networks." Entropy 24, no. 1 (December 21, 2021): 7. http://dx.doi.org/10.3390/e24010007.

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Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g., state of neurons) and slow-changing trainable variables (e.g., weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of neurons is fixed, and by the Schrodinger equation, if the learning system is capable of adjusting its own parameters such as the number of neurons, step size and mini-batch size. We argue that the Lorentz symmetries and curved space-time can emerge from the interplay between stochastic entropy production and entropy destruction due to learning. We show that the non-equilibrium dynamics of non-trainable variables can be described by the geodesic equation (in the emergent space-time) for localized states of neurons, and by the Einstein equations (with cosmological constant) for the entire network. We conclude that the quantum description of trainable variables and the gravitational description of non-trainable variables are dual in the sense that they provide alternative macroscopic descriptions of the same learning system, defined microscopically as a neural network.
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Costanza, G. "Non-Markovian stochastic evolution equations." Physica A: Statistical Mechanics and its Applications 402 (May 2014): 224–35. http://dx.doi.org/10.1016/j.physa.2014.01.038.

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Adamian, G. G., N. V. Antonenko, Z. Kanokov, and V. V. Sargsyan. "Quantum Non-Markovian Stochastic Equations." Theoretical and Mathematical Physics 145, no. 1 (October 2005): 1443–56. http://dx.doi.org/10.1007/s11232-005-0170-2.

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Semina, I., V. Semin, F. Petruccione, and A. Barchielli. "Stochastic Schrödinger Equations for Markovian and non-Markovian Cases." Open Systems & Information Dynamics 21, no. 01n02 (March 12, 2014): 1440008. http://dx.doi.org/10.1142/s1230161214400083.

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Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples — the damped harmonic oscillator and a two-level atom with homodyne photodetection. We then consider how to introduce memory effects in the stochastic Schrödinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit.
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Li, Xiantao. "Markovian embedding procedures for non-Markovian stochastic Schrödinger equations." Physics Letters A 387 (January 2021): 127036. http://dx.doi.org/10.1016/j.physleta.2020.127036.

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Tilloy, Antoine. "Time-local unraveling of non-Markovian stochastic Schrödinger equations." Quantum 1 (September 19, 2017): 29. http://dx.doi.org/10.22331/q-2017-09-19-29.

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Non-Markovian stochastic Schrödinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.
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Farias, R. L. S., Rudnei O. Ramos, and L. A. da Silva. "Numerical solutions for non-Markovian stochastic equations of motion." Computer Physics Communications 180, no. 4 (April 2009): 574–79. http://dx.doi.org/10.1016/j.cpc.2008.12.005.

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Gough, John E., Matthew R. James, and Hendra I. Nurdin. "Single photon quantum filtering using non-Markovian embeddings." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5408–21. http://dx.doi.org/10.1098/rsta.2011.0524.

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We determine quantum master and filter equations for continuous measurement of systems coupled to input fields in certain non-classical continuous-mode states, specifically single photon states. The quantum filters are shown to be derivable from an embedding into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.
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Breuer, Heinz-Peter, Bernd Kappler, and Francesco Petruccione. "Stochastic wave-function method for non-Markovian quantum master equations." Physical Review A 59, no. 2 (February 1, 1999): 1633–43. http://dx.doi.org/10.1103/physreva.59.1633.

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Sezer, Ali Devin, Thomas Kruse, and Alexandre Popier. "Backward stochastic differential equations with non-Markovian singular terminal values." Stochastics and Dynamics 19, no. 02 (March 27, 2019): 1950006. http://dx.doi.org/10.1142/s0219493719500060.

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We solve a class of BSDE with a power function [Formula: see text], [Formula: see text], driving its drift and with the terminal boundary condition [Formula: see text] (for which [Formula: see text] is assumed) or [Formula: see text], where [Formula: see text] is the ball in the path space [Formula: see text] of the underlying Brownian motion centered at the constant function [Formula: see text] and radius [Formula: see text]. The solution involves the derivation and solution of a related heat equation in which [Formula: see text] serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain, the BSDE has continuous sample paths with the prescribed terminal value.
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Dissertations / Theses on the topic "Non-markovian stochastic Schrodinger equations"

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Gambetta, Jay, and n/a. "Non-Markovian Stochastic Schrodinger Equations and Interpretations of Quantum Mechanics." Griffith University. School of Science, 2004. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20040429.141303.

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It has been almost eighty years since quantum mechanics emerged as a complete theory, yet debates about how should quantum mechanics be interpreted still occur. Interpretations are many and varied, some taking us as fundamental in determining reality (orthodox interpretation), while others proposing that reality exists outside of us, but it is a lot more complicated than that implied by classical mechanics. In this thesis I am going to try to provide new light on this debate by investigating dynamics under both the orthodox and modal interpretation. In particular I will answer the question what is the interpretation of non-Markovian stochastic Schrodinger equations? I conclude that under the orthodox view these equations have only a numerical interpretation. They provide a rule for calculating the state of the system at time t if we made a measurement on the bath (a collection of oscillators {ak}) at that time, yielding results {zk}. However in the modal view they have a meaning: non-Markovian stochastic Schrodinger equations represent the evolution of the system part of the property state of the universe (bath + system).
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Gambetta, Jay. "Non-Markovian Stochastic Schrodinger Equations and Interpretations of Quantum Mechanics." Thesis, Griffith University, 2004. http://hdl.handle.net/10072/366271.

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It has been almost eighty years since quantum mechanics emerged as a complete theory, yet debates about “how should quantum mechanics be interpreted” still occur. Interpretations are many and varied, some taking us as fundamental in determining reality (orthodox interpretation), while others proposing that reality exists outside of us, but it is a lot more complicated than that implied by classical mechanics. In this thesis I am going to try to provide new light on this debate by investigating dynamics under both the orthodox and modal interpretation. In particular I will answer the question what is the interpretation of non-Markovian stochastic Schrodinger equations? I conclude that under the orthodox view these equations have only a numerical interpretation. They provide a rule for calculating the state of the system at time t if we made a measurement on the bath (a collection of oscillators {ak}) at that time, yielding results {zk}. However in the modal view they have a meaning: non-Markovian stochastic Schrodinger equations represent the evolution of the system part of the property state of the universe (bath + system).
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Science
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Books on the topic "Non-markovian stochastic Schrodinger equations"

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Chekroun, Mickaël D., Honghu Liu, and Shouhong Wang. Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12520-6.

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Wang, Shouhong, Mickaël D. D. Chekroun, and Honghu Liu. Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations: Stochastic Manifolds for Nonlinear SPDEs II. Springer, 2014.

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Wang, Shouhong, Honghu Liu, and Mickaël D. Chekroun. Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations: Stochastic Manifolds for Nonlinear SPDEs II. Springer, 2014.

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Strasberg, Philipp. Quantum Stochastic Thermodynamics. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192895585.001.0001.

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Abstract Processes at the nanoscale happen far away from the thermodynamic limit, far from equilibrium and are dominated by fluctuations and, perhaps, even quantum effects. This book establishes a consistent thermodynamic framework for such processes by combining tools from non-equilibrium statistical mechanics and the theory of open quantum systems. The book is accessible for graduate students and of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability. It puts most emphasis on the microscopic derivation and understanding of key principles and concepts as well as their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon and time-reversal symmetry, among other topics. Furthermore, the book treats a few applications in detail to illustrate the general theory and its potential for practical applications. These are single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser and related set-ups in quantum optics.
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Book chapters on the topic "Non-markovian stochastic Schrodinger equations"

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Chekroun, Mickaël D., Honghu Liu, and Shouhong Wang. "Non-Markovian Stochastic Reduced Equations." In SpringerBriefs in Mathematics, 59–71. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12520-6_5.

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Chekroun, Mickaël D., Honghu Liu, and Shouhong Wang. "Non-Markovian Stochastic Reduced Equations on the Fly." In SpringerBriefs in Mathematics, 85–112. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12520-6_7.

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Leimkuhler, Benedict, and Matthias Sachs. "Ergodic Properties of Quasi-Markovian Generalized Langevin Equations with Configuration Dependent Noise and Non-conservative Force." In Stochastic Dynamics Out of Equilibrium, 282–330. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15096-9_8.

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El-Tawil, Magdy A. "The Average Solution of a Stochastic Nonlinear Schrodinger Equation under Stochastic Complex Non-homogeneity and Complex Initial Conditions." In Transactions on Computational Science III, 143–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00212-0_8.

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"Markovian and Non-Markovian Solutions of Stochastic Nonlinear Differential Equations." In Nonlinear Random Vibration, 19–34. CRC Press, 2011. http://dx.doi.org/10.1201/b11614-3.

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Strasberg, Philipp. "Quantum Thermodynamics Without Measurements." In Quantum Stochastic Thermodynamics, 104–74. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192895585.003.0003.

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Abstract We derive the basic laws of phenomenological non-equilibrium thermodynamics for small open systems, whose quantum nature can no longer be neglected. Emphasis is put from the beginning on deriving them from an underlying microscopic system on deriving them from an underlying microscopic system–bath picture. Commonly considered approximation schemes (wea k coupling master equations) are reviewed and their thermodynamics is studied. The zeroth law is discussed for small systems and exact identities for the entropy production, valid at strong coupling and in the non non-Markovian regime, are introduced. We discu ss the effect of finite baths even out of equilibrium and use the framework of repeated interactions to study microscopic non-equilibrium resources. The chapter concludes with the study of particle transport and thermoelectric devices, which were realized in experiments. This chapter focuses entirely on the dynamics of a system coupled to a bath without any external interventions.
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Conference papers on the topic "Non-markovian stochastic Schrodinger equations"

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Gambetta, Jay M., and Howard M. Wiseman. "A non-Markovian stochastic Schrodinger equation developed from a hidden variable interpretation." In SPIE's First International Symposium on Fluctuations and Noise, edited by Derek Abbott, Jeffrey H. Shapiro, and Yoshihisa Yamamoto. SPIE, 2003. http://dx.doi.org/10.1117/12.496938.

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Moeller, Lothar. "Stochastic Anti-symmetric Schrodinger Equations for Non-Manakovian Propagation." In 2020 European Conference on Optical Communications (ECOC). IEEE, 2020. http://dx.doi.org/10.1109/ecoc48923.2020.9333375.

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El‐Tawil, Magdy A. "On Stochastic Nonlinear Schrodinger Equations under Stochastic Complex Non‐Homogeneity and Complex Initial Conditions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991101.

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Wang, Guoqiang, and Donglong Li. "Algorithmic Analysis of Euler-Maruyama Scheme for Stochastic Differential Delay Equations with Markovian Switching and Poisson Jump, under Non-Lipschitz Condition." In 2009 Fifth International Conference on Natural Computation. IEEE, 2009. http://dx.doi.org/10.1109/icnc.2009.54.

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Caleyo, F., J. C. Vela´zquez, J. M. Hallen, A. Valor, and A. Esquivel-Amezcua. "Markov Chain Model Helps Predict Pitting Corrosion Depth and Rate in Underground Pipelines." In 2010 8th International Pipeline Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ipc2010-31351.

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A continuous-time, non-homogenous pure birth Markov chain serves to model external pitting corrosion in buried pipelines. The analytical solution of Kolmogorov’s forward equations for this type of Markov process gives the transition probability function in a discrete space of pit depths. The transition probability function can be completely identified by making a correlation between the stochastic pit depth mean and the deterministic mean obtained experimentally. Previously reported Monte Carlo simulations have been used for the prediction of the evolution of the pit depth distribution mean value with time for different soil types. The simulated pit depth distributions are used to develop a stochastic model based on Markov chains to predict the progression of pitting corrosion depth and rate distributions from the observed soil properties and pipeline coating characteristics. The proposed model can also be applied to pitting corrosion data from repeated in-line pipeline inspections. Real-life case studies presented in this work show how pipeline inspection and maintenance planning can be improved through the use of the proposed Markovian model for pitting corrosion.
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