Locating the Many-Body transition via the von Neumann entropy

2014 ◽  
Author(s):  
M. Pino ◽  
M. Ortuño ◽  
A. M. Somoza ◽  
J. Prior
Keyword(s):  
Von Neumann Entropy ◽  
Many Body ◽  
Von Neumann ◽  
The Many

scholarly journals ENTANGLEMENT PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4041-4057
Author(s):  
J. W. CLARK ◽  
A. MANDILARA ◽  
M. L. RISTIG ◽  
K. E. KÜRTEN
Keyword(s):  
Quantum Phase Transitions ◽  
Body Wave ◽  
Wave Functions ◽  
Von Neumann Entropy ◽  
Many Body ◽  
Lattice Systems ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Many Body Systems ◽  
The One

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

scholarly journals The Correlation Production in Thermodynamics

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 111 ◽  
Author(s):  
Sheng-Wen Li
Keyword(s):  
Open System ◽  
Open Systems ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Many Body ◽  
Particle Collisions ◽  
Von Neumann ◽  
Entropy Increase ◽  
Many Body Systems ◽  
The Many

Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite confusing compared with the macroscopic irreversibility. We notice that indeed the macroscopic entropy increase in standard thermodynamics is associated with the correlation production inside the full ensemble state of the whole system. In open systems, the irreversible entropy production of the open system can be proved to be equivalent with the correlation production between the open system and its environment. During the free diffusion of an isolated ideal gas, the correlation between the spatial and momentum distributions is increasing monotonically, and it could well reproduce the entropy increase result in standard thermodynamics. In the presence of particle collisions, the single-particle distribution always approaches the Maxwell-Boltzmann distribution as its steady state, and its entropy increase indeed indicates the correlation production between the particles. In all these examples, the total entropy of the whole isolated system keeps constant, while the correlation production reproduces the irreversible entropy increase in the standard macroscopic thermodynamics. In this sense, the macroscopic irreversibility and the microscopic reversibility no longer contradict with each other.

scholarly journals Many-Body Systems and Quantum Chaos: The Multiparticle Quantum Arnol’d Cat

2019 ◽  
Vol 4 (3) ◽  
pp. 72
Author(s):  
Giorgio Mantica
Keyword(s):  
Hamiltonian System ◽  
Density Matrix ◽  
Quantum Chaos ◽  
Reduced Density Matrix ◽  
Von Neumann Entropy ◽  
Physical Parameters ◽  
Many Body ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

A multi-particle extension of the Arnol’d cat Hamiltonian system is presented, which can serve as a fully dynamical model of decoherence. The behavior of the von Neumann entropy of the reduced density matrix is studied, in time and as a function of the physical parameters, with special regard to increasing the mass of the cat particle.

scholarly journals Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 382
Author(s):  
Frank Schäfer ◽  
Miguel A. Bastarrachea-Magnani ◽  
Axel U. J. Lode ◽  
Laurent de Forges de Parny ◽  
Andreas Buchleitner
Keyword(s):  
Initial Conditions ◽  
Dynamical Behavior ◽  
Particle Interaction ◽  
Interaction Strength ◽  
Von Neumann Entropy ◽  
Spectral Structure ◽  
Many Body ◽  
Point Energy ◽  
Von Neumann ◽  
Body Dynamics

We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior of the particles launched either at the single-particle ground state or saddle-point energy, in a time-independent potential. We complement these results by a characterization of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time evolution of a single particle’s von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X)—which also allows us to extrapolate our results for increasing particle numbers.

scholarly journals Dynamical manifestations of quantum chaos: correlation hole and bulge

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160434 ◽  
Author(s):  
E. J. Torres-Herrera ◽  
Lea F. Santos
Keyword(s):  
Quantum Chaos ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Direct Access ◽  
Many Body ◽  
Initial State ◽  
Von Neumann ◽  
Interacting Systems ◽  
Correlation Hole ◽  
The Many

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable–chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

On the many-body theory of nuclear reactions

1968 ◽  
Vol 111 (1) ◽  
pp. 392-416 ◽  
Author(s):  
K DIETRICH ◽  
K HARA
Keyword(s):  
Nuclear Reactions ◽  
Many Body ◽  
Many Body Theory ◽  
The Many ◽  
Body Theory

Revealing the many-body interactions and valley-polarization behavior in Re-doped MoS2 monolayers

2021 ◽  
Vol 118 (11) ◽  
pp. 113101
Author(s):  
Xiaoli Zhu ◽  
Siting Ding ◽  
Lihui Li ◽  
Ying Jiang ◽  
Biyuan Zheng ◽  
...  
Keyword(s):  
Many Body ◽  
Polarization Behavior ◽  
Valley Polarization ◽  
Mos2 Monolayers ◽  
The Many ◽  
Many Body Interactions
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