scholarly journals A Large Deviation Principle in Many-Body Quantum Dynamics

2021 ◽  
Author(s):  
Kay Kirkpatrick ◽  
Simone Rademacher ◽  
Benjamin Schlein
Keyword(s):  
Quantum Dynamics ◽  
Limit Theorems ◽  
Large Deviation ◽  
Mean Field ◽  
Quantum Evolution ◽  
Many Body ◽  
Many Body Quantum Dynamics ◽  
The Mean ◽  
The Many ◽  
Mean Field Regime

AbstractWe consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates that are consistent with central limit theorems that have been established in the last years.

Elementary Principles

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Large Deflection ◽  
Mean Field ◽  
Distribution Functions ◽  
Many Body ◽  
Many Body Theory ◽  
Binary Correlation ◽  
The Mean ◽  
The Many ◽  
Body Theory

The many-body theory combines ideas of thermodynamics with ideas of mechanics. In this introductory chapter, the symbiosis of these two different fields of physics is demonstrated on overly simplified models. We explore the principles of finite-range forces to show the twofold nature of virial corrections. Infrequent collisions with a large deflection angle lead to collision integrals and rather frequent encounters with deflections on small angles act as a mean field. The (mean-field) corrections to drift result in the internal pressure and the nonlocal correction to the collisions results in the effect of the molecular volumes. The concept of distribution functions is introduced and the measure of information as entropy. The binary correlation allows one to distinguish tails and cores of the interaction potential. The concept of binary correlation is thus behind the intuitive picture of the kinetic equation.

scholarly journals Quench dynamics of a disordered array of dissipative coupled cavities

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140328 ◽  
Author(s):  
C. Creatore ◽  
R. Fazio ◽  
J. Keeling ◽  
H. E. Türeci
Keyword(s):  
Mean Field ◽  
Many Body ◽  
Coupled Cavities ◽  
Fock State ◽  
The Mean ◽  
Quench Dynamics ◽  
The Many

We investigate the mean-field dynamics of a system of interacting photons in an array of coupled cavities in the presence of dissipation and disorder. We follow the evolution of an initially prepared Fock state, and show how the interplay between dissipation and disorder affects the coherence properties of the cavity emission, and show that these properties can be used as signatures of the many-body phase of the whole array.

scholarly journals Correlated Magnetoexcitons in Semiconductor Quantum Dots at Finite Temperature

1999 ◽  
Vol 579 ◽  
Author(s):  
D.J. Dean ◽  
M.R. Strayer ◽  
J.C. Wells
Keyword(s):  
Quantum Dots ◽  
High Performance ◽  
Theoretical Study ◽  
Mean Field ◽  
Semiconductor Quantum Dots ◽  
Many Body ◽  
Hartree Fock ◽  
The Mean ◽  
Numerical Precision ◽  
The Many

ABSTRACTWe describe computational methods for the theoretical study of explicit correlations beyond the mean field in excitons confined in semiconductor quantum dots in terms of the Auxiliary-Field Monte Carlo (AFMC) method [1]. Using AFMC, the many-body problem is formulated as a Feynman path integral at finite temperatures and evaluated to numerical precision. This approach is ideally suited for implementation on high-performance parallel computers. Our strategy is to generate a set of mean-field states via the Hartree-Fock method for use as a basis for the AFMC calculations. We present preliminary results.

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

scholarly journals Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1342
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Infinite Number ◽  
Mean Field ◽  
Solvable Model ◽  
Time Dependent ◽  
Angular Momentum Operator ◽  
Many Body ◽  
The Many ◽  
Bose Einstein ◽  
Number Of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

scholarly journals A multi-class extension of the mean field Bolker–Pacala population model

2018 ◽  
Vol 26 (3) ◽  
pp. 163-174 ◽  
Author(s):  
Mariya Bessonov ◽  
Stanislav Molchanov ◽  
Joseph Whitmeyer
Keyword(s):  
Population Model ◽  
Limit Theorems ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Geometric Ergodicity ◽  
Equilibrium Solutions ◽  
The Mean ◽  
Number Of Classes ◽  
Population Suppression

Abstract We extend our earlier mean field approximation of the Bolker–Pacala model of population dynamics by dividing the population into N classes, using a mean field approximation for each class but also allowing migration between classes as well as possibly suppressive influence of the population of one class over another class. For {N\geq 2} , we obtain one symmetric nontrivial equilibrium for the system and give global limit theorems. For {N=2} , we calculate all equilibrium solutions, which, under additional conditions, include multiple nontrivial equilibria. Lastly, we prove geometric ergodicity regardless of the number of classes when there is no population suppression across the classes.

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