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Quantum system
About: Quantum system is a research topic. Over the lifetime, 10305 publications have been published within this topic receiving 241445 citations.
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TL;DR: In this paper, the authors describe the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations, and the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.
Abstract: This chapter describes the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations. But the physical world is quantum mechanical, and therefore the proper problem is the simulation of quantum physics. A computer which will give the same probabilities as the quantum system does. The present theory of physics allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition is right, physical law is wrong. Quantum theory and quantizing is a very specific type of theory. The chapter talks about the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature. There are interesting philosophical questions about reasoning, and relationship, observation, and measurement and so on, which computers have stimulated people to think about anew, with new types of thinking.
7,202 citations
TL;DR: It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.
Abstract: We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture. Berry's conjecture is expected to hold only if the corresponding classical system is chaotic, and essentially states that the energy eigenfunctions behave as if they were Gaussian random variables. We review the existing evidence, and show that previously neglected effects substantially strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas as an explicit example of a many-body system which is known to be classically chaotic, and show that an energy eigenstate which obeys Berry's conjecture predicts a Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac distribution for the momentum of each constituent particle, depending on whether the wave functions are taken to be nonsymmetric, completely symmetric, or completely antisymmetric functions of the positions of the particles. We call this phenomenon eigenstate thermalization. We show that a generic initial state will approach thermal equilibrium at least as fast as O(\ensuremath{\Elzxh}/\ensuremath{\Delta})${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$, where \ensuremath{\Delta} is the uncertainty in the total energy of the gas. This result holds for an individual initial state; in contrast to the classical theory, no averaging over an ensemble of initial states is needed. We argue that these results constitute a sound foundation for quantum statistical mechanics.
2,649 citations
TL;DR: It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.
Abstract: It is demonstrated that an isolated generic quantum many-body system does relax to a state well described by the standard statistical mechanical prescription The thermalization happens at the level of individual eigenstates, allowing the computation of thermal averages from knowledge of any eigenstate in the microcanonical energy window An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive Recently, meaningful experimental studies1,2 of the problem have become possible, stimulating theoretical interest3,4,5,6,7 In generic isolated systems, non-equilibrium dynamics is expected8,9 to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible10 For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete11 Some recent studies4,5 even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch12 and Srednicki13 A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result
2,598 citations
TL;DR: In this article, an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two nonzero eigenvalues was given, and evidence suggests that the formula is valid for all states of this system.
Abstract: The ``entanglement of formation'' of a mixed state \ensuremath{\rho} of a bipartite quantum system can be defined as the minimum number of singlets needed to create an ensemble of pure states that represents \ensuremath{\rho}. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two nonzero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.
2,386 citations
TL;DR: In this paper, a formalism has been developed, using Feynman's space-time formulation of nonrelativistic quantum mechanics whereby the behavior of a system of interest, which is coupled to other external quantum systems, may be calculated in terms of its own variables only.
2,288 citations