scholarly journals Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring

2014 ◽  
Vol 28 (30) ◽  
pp. 1550021 ◽  
Author(s):  
Kang-Soo Lee ◽  
Uwe R. Fischer
Keyword(s):  
Variational Principle ◽  
Temporal Evolution ◽  
Field Operator ◽  
Error Monitoring ◽  
Many Body ◽  
Body State ◽  
Body Dynamics ◽  
Self Consistent ◽  
The Many ◽  
Trial State

We develop a method to describe the temporal evolution of an interacting system of bosons, for which the field operator expansion is truncated after a finite number M of modes, in a rigorously controlled manner. Using McLachlan's principle of least error, we find a self-consistent set of equations for the many-body state. As a particular benefit and in distinction to previously proposed approaches, the presently introduced method facilitates the dynamical increase of the number of orbitals during the temporal evolution, due to the fact that we can rigorously monitor the error made by increasing the truncation dimension M. The additional orbitals, determined by the condition of least error of the truncated evolution relative to the exact one, are obtained from an initial trial state by steepest constrained descent.

Many-body Green functions in nuclear physics

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740025 ◽  
Author(s):  
J. Speth ◽  
N. Lyutorovich
Keyword(s):  
Nuclear Physics ◽  
Green Functions ◽  
Many Body ◽  
General Applicability ◽  
Pair Correlations ◽  
Self Consistent ◽  
The Many ◽  
The One ◽  
General Relations ◽  
Three Body

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

scholarly journals Entropy Production Within a Pulsed Bose–Einstein Condensate

2016 ◽  
Vol 71 (10) ◽  
pp. 875-881 ◽  
Author(s):  
Christoph Heinisch ◽  
Martin Holthaus
Keyword(s):  
Einstein Condensate ◽  
Many Body ◽  
Initial State ◽  
Site Model ◽  
Bose Einstein Condensate ◽  
Body Dynamics ◽  
Adiabatic Motion ◽  
The Many ◽  
Bose Einstein ◽  
Loss Of Coherence

AbstractWe suggest to subject anharmonically trapped Bose–Einstein condensates to sinusoidal forcing with a smooth, slowly changing envelope, and to measure the coherence of the system after such pulses. In a series of measurements with successively increased maximum forcing strength, one then expects an adiabatic return of the condensate to its initial state as long as the pulses remain sufficiently weak. In contrast, once the maximum driving amplitude exceeds a certain critical value there should be a drastic loss of coherence, reflecting significant heating induced by the pulse. This predicted experimental signature is traced to the loss of an effective adiabatic invariant, and to the ensuing breakdown of adiabatic motion of the system’s Floquet state when the many-body dynamics become chaotic. Our scenario is illustrated with the help of a two-site model of a forced bosonic Josephson junction, but should also hold for other, experimentally accessible configurations.

scholarly journals Isospin dynamics in nuclear structure

2018 ◽  
Vol 182 ◽  
pp. 02075
Author(s):  
Elena Litvinova ◽  
Caroline Robin ◽  
Peter Schuck
Keyword(s):  
Nucleon Nucleon ◽  
Many Body ◽  
Rare Isotope ◽  
Rare Isotope Beam ◽  
Theoretical Approaches ◽  
Energy Part ◽  
Body Dynamics ◽  
Nucleon Nucleon Interaction ◽  
The Many ◽  
Nuclear Response

We discuss some special aspects of the nuclear many-body problem related to isospin transfer. The major quantity of interest is the in-medium propagator of a particlehole configuration of the proton-neutron character, which determines the nuclear response to isospin transferring external fields. One of the most studied excitation modes is the Gamow-Teller resonance (GTR), which can, therefore, be used as a sensitive test for the theoretical approaches. Its low-energy part, which is responsible for the beta decay halflives, is especially convenient for this. Models benchmarked against the GTR can be used to predict other, more exotic, excitations studied at nuclear rare isotope beam facilities and in astrophysics. As far as the precision is concerned, the major problem in such an analysis is to disentangle the effects related to the underlying interaction and those caused by the many-body correlations. Therefore, approaches (i) based on fundamental concepts for the nucleon-nucleon interaction which (ii) include complex many-body dynamics are the preferred ones. We discuss progress and obstacles on the way to such approaches.

On Permanent Rotations of a System of Two Coupled Gyrostats in a Central Newtonian Force Field

2015 ◽  
Author(s):  
Dmitriy Chebanov ◽  
Jose A. Salas
Keyword(s):  
Force Field ◽  
Vertical Axis ◽  
Many Body ◽  
Newtonian Force ◽  
Body Dynamics ◽  
A Chain ◽  
The Many ◽  
The One ◽  
Permanent Rotations ◽  
Newtonian Force Field

This paper studies the problem of the motion of a chain of two gyrostats coupled by an ideal spherical joint. The chain moves about a fixed point in a central Newtonian force field. Under the assumption that the gyrostatic moment of each gyrostat is constant relative to its carrier, the paper establishes and analyzes the conditions for existence of the chain’s permanent rotations about a vertical axis. For a case when each gyrostat has the mass distribution analogous to the one of a Lagrange gyroscope, the paper derives and analyzes the necessary conditions for stability of the permanent rotations. The findings of the paper extend corresponding results in the dynamics of a single gyrostat to a case of the multibody chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.

scholarly journals Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 392
Author(s):  
Axel U. J. Lode ◽  
Sunayana Dutta ◽  
Camille Lévêque
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Time Dependent ◽  
Gauge Fields ◽  
Single Shot ◽  
Body Density ◽  
Many Body ◽  
Atomic Systems ◽  
Body State ◽  
The Many

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.

scholarly journals Exploring the Many-Body Dynamics Near a Conical Intersection with Trapped Rydberg Ions

2021 ◽  
Vol 126 (23) ◽  
Author(s):  
Filippo M. Gambetta ◽  
Chi Zhang ◽  
Markus Hennrich ◽  
Igor Lesanovsky ◽  
Weibin Li
Keyword(s):  
Conical Intersection ◽  
Many Body ◽  
Body Dynamics ◽  
The Many

scholarly journals QUANTUM MATTERS: PHYSICS BEYOND LANDAU'S PARADIGMS

2006 ◽  
Vol 20 (19) ◽  
pp. 2603-2611 ◽  
Author(s):  
T. SENTHIL
Keyword(s):  
Particle Physics ◽  
Order Parameter ◽  
Theoretical Work ◽  
Many Body ◽  
General Validity ◽  
Quasiparticle Excitation ◽  
Body State ◽  
Growing Body ◽  
The Many ◽  
Theoretical Developments

Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter to distinguish different states of matter. Experiments in a number of correlated materials raise serious suspicions about the general validity of either notion. A growing body of theoretical work has confirmed these suspicions, and explored physics beyond Landau's paradigms. This article provides an overview of some of these theoretical developments.

scholarly journals Beyond mean-field dynamics in closed and open bosonic systems

2013 ◽  
Author(s):  
Γεώργιος Κορδάς
Keyword(s):  
Mean Field ◽  
Einstein Condensation ◽  
Many Body ◽  
Practical Applications ◽  
Body Dynamics ◽  
Systematic Development ◽  
The Many ◽  
Bose Einstein ◽  
State Path ◽  
Present Thesis

The present thesis is devoted to the dynamics in open or closed manybodybosonic systems, with the use of beyond mean-eld methods.In the rst part, inspired by the state-of-the-art experiments, we study thedynamics of a Bose-Einstein condensation which is loaded in an optical latticewith localized loss channels for the atoms. We prove that the particularform of the dissipation can help us to control the many-body dynamics. Theloss allows the local manipulation of the system's coherence properties andcreates attractive xed points in the classical (mean-eld) phase space. Wepredict the dynamical creation of stable nonlinear structures like discretebright and dark solitons. Furthermore, for specic initial states, the systemsproduces highly entangled and long-living states, which are of high relevancefor practical applications. The rst part of this thesis ends with the study ofnon-equilibrium bosonic transport across optical one-dimensional lattices.In the second part, we present techniques for bosonic many-body systemswhich are based on path integrals. We analyze the Bose-Einstein condensationphenomenon by using tools from quantum information theory and eldtheory. Finally, we introduce a coherent state path integral formalism inthe continuum, which allows us the systematic development of approximatemethods for the study of bosons in optical lattices.

scholarly journals Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

2015 ◽  
Vol 29 (18) ◽  
pp. 1530010 ◽  
Author(s):  
A. L. Kuzemsky
Keyword(s):  
Free Energy ◽  
Variational Principle ◽  
Free Energies ◽  
Many Body ◽  
Hubbard Models ◽  
Self Consistent Field ◽  
Mean Fields ◽  
Interacting Systems ◽  
The Many ◽  
Statistical Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising, Heisenberg and Hubbard models, superconducting (SC) and superfluid systems, etc. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects and for those who are interested in concrete applications.

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