Wave equation for dissipative systems derived from a quantized many-body problem

1980 ◽  
Vol 58 (7) ◽  
pp. 1019-1025 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Body Wave ◽  
Time Dependent ◽  
Dissipative Systems ◽  
Many Body ◽  
Dependent Part ◽  
The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

scholarly journals Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation

1997 ◽  
Vol 08 (04) ◽  
pp. 705-716 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Washington Taylor
Keyword(s):  
Schrödinger Equation ◽  
Arbitrary Number ◽  
Schrodinger Equation ◽  
Lattice Gas ◽  
Quantum Computer ◽  
Many Body ◽  
Lattice Gas Models ◽  
Many Body Systems ◽  
The Many ◽  
Classical Computer

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrödinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrödinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.

scholarly journals Angular distribution of scission neutrons studied with time-dependent Schrödinger equation

2018 ◽  
Vol 169 ◽  
pp. 00029
Author(s):  
Takahiro Wada ◽  
Tomomasa Asano ◽  
Nicolae Carjan
Keyword(s):  
Wave Function ◽  
Angular Distribution ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Schrodinger Equation ◽  
Initial Distribution ◽  
Time Dependent ◽  
Heavy Fragment ◽  
Fission Fragments ◽  
Asymmetric Fission

We investigate the angular distribution of scission neutrons taking account of the effects of fission fragments. The time evolution of the wave function of the scission neutron is obtained by integrating the time-dependent Schrodinger equation numerically. The effects of the fission fragments are taken into account by means of the optical potentials. The angular distribution is strongly modified by the presence of the fragments. In the case of asymmetric fission, it is found that the heavy fragment has stronger effects. Dependence on the initial distribution and on the properties of fission fragments is discussed. We also discuss on the treatment of the boundary to avoid artificial reflections

scholarly journals Hybrid nature of the abnormal solutions of the Bethe–Salpeter equation in the Wick–Cutkosky model

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
J. Carbonell ◽  
V. A. Karmanov ◽  
H. Sazdjian
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Form Factors ◽  
Massless Particle ◽  
Ladder Approximation ◽  
Many Body ◽  
Relativistic Limit ◽  
Elastic Form ◽  
The Many

AbstractIn the Wick–Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe–Salpeter equation has solutions of two types, called “normal” and “abnormal”. In the non-relativistic limit, the normal solutions correspond to the usual Coulomb spectrum, whereas the abnormal ones do not have non-relativistic counterparts – they are absent in the Schrödinger equation framework. We have studied, in the formalism of the light-front dynamics, the Fock-space content of the abnormal solutions. It turns out that, in contrast to the normal ones, the abnormal states are dominated by the massless exchange particles (by 90 % or more), what provides a natural explanation of their decoupling from the two-body Schrödinger equation. Assuming that one of the massive constituents is charged, we have calculated the electromagnetic elastic form factors of the normal and abnormal states, as well as the transition form factors. The results on form factors confirm the many-body nature of the abnormal states, as found from the Fock-space analysis. The abnormal solutions have thus properties similar to those of hybrid states, made here essentially of two massive constituents and several or many massless exchange particles. They could also be interpreted as the Abelian scalar analogs of the QCD hybrid states. The question of the validity of the ladder approximation of the model is also examined.

scholarly journals Approximating Ground States by Neural Network Quantum States

2018 ◽  
Author(s):  
Ying Yang ◽  
Chengyang Zhang ◽  
Huaixin Cao
Keyword(s):  
Neural Network ◽  
Relative Error ◽  
Ground State ◽  
Quantum Physics ◽  
Body Problem ◽  
Body Wave ◽  
Quantum States ◽  
Many Body ◽  
The Many ◽  
Exponential Complexity

The many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Motivated by the Giuseppe Carleo's work titled solving the quantum many-body problem with artificial neural networks [Science, 2017, 355: 602], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian $H$ in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

EFFECTIVE MASS HAMILTONIANS WITH LINEAR TERMS IN THE MOMENTUM: DARBOUX TRANSFORMATIONS AND FORM-PRESERVING TRANSFORMATIONS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1735-1769 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Darboux Transformations

We define form-preserving transformations and Darboux transformations for time-dependent, effective mass Hamiltonians with additional linear terms. We give reality conditions for both transformations, guaranteeing the transformed potential to be real-valued. We further show that our form-preserving transformation preserves normalizability of the Schrödinger wave function. Our results generalize all former results on form-preserving transformations and Darboux transformations for the time-dependent Schrödinger equation. This paper is a sequel of Refs. 16–18.

scholarly journals Fidelity and Entropy Production in Quench Dynamics of Interacting Bosons in an Optical Lattice

2019 ◽  
Vol 1 (2) ◽  
pp. 304-316 ◽  
Author(s):  
Rhombik Roy ◽  
Camille Lévêque ◽  
Axel U. J. Lode ◽  
Arnaldo Gammal ◽  
Barnali Chakrabarti
Keyword(s):  
Optical Lattice ◽  
Quantum Phase Transitions ◽  
Body Wave ◽  
Time Dependent ◽  
Strong Interactions ◽  
Relaxation Processes ◽  
Many Body ◽  
Wide Range ◽  
The Many ◽  
Quantum Fidelity

We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We report the time evolution of three key quantities, namely, the occupations of the natural orbitals, that is, the eigenvalues of the one-body reduced density matrix, the many-body Shannon information entropy, and the quantum fidelity for a wide range of interactions. Our key motivation is to characterize relaxation processes where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values via the quantum fidelity and via the production of many-body entropy. The interaction, as a parameter, can induce a phase transition in the ground state of the system from a superfluid (SF) state to a Mott-insulator (MI) state. We show that, for a quench to a weak interaction, the fidelity remains close to unity and the entropy exhibits oscillations. Whereas for a quench to strong interactions (SF to MI transition), the relaxation process is characterized by the first collapse of the quantum fidelity and entropy saturation to an equilibrium value. The dip and the non-analytic nature of quantum fidelity is a hallmark of dynamical quantum phase transitions. We quantify the characteristic time at which the quantum fidelity collapses and the entropy saturates.

Quantum tunneling in a dissipative environment

1992 ◽  
Vol 70 (9) ◽  
pp. 719-730 ◽  
Author(s):  
M. Hron ◽  
M. Razavy
Keyword(s):  
Wave Equation ◽  
Schrödinger Equation ◽  
Quantum Tunneling ◽  
Schrodinger Equation ◽  
Quantum Coherence ◽  
Harmonic Oscillators ◽  
Dissipative Systems ◽  
Many Body ◽  
Coupled Equations ◽  
Central Particle

A wave equation formulation of the problem of quantum tunneling in a dissipative medium is developed by considering a many-body system in which the central particle is subject to an arbitrary force law, and at the same time is coupled to a bath of noninteracting harmonic oscillators. For the motion of the central particle it is possible to obtain an effective Lagrangian and Hamiltonian by eliminating the degrees of freedom of the oscillators. However both of these operators are nonlocal, and it is difficult to derive a wave equation for this motion. As an alternative method one can write a many-body Schrödinger equation for the whole system, and then eliminate the wave functions of all of the oscillators. This result is a many-channel Schrödinger equation for the motion of the central particle. By truncating this set of coupled equations, one can solve the problem for different force laws. In particular, in this work, the cases of dissipative tunneling, hopping, and quantum coherence are studied in detail. It is also shown how this approach can be generalized to multidimensional dissipative systems.

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