scholarly journals Emergence of Network Bifurcation Triggered by Entanglement

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 147
Author(s):  
Xi Yong ◽  
Man-Hong Yung ◽  
Xue-Ke Song ◽  
Xun Gao ◽  
Angsheng Li
Keyword(s):  
Equilibrium State ◽  
Plasma Oscillation ◽  
Coarse Grained ◽  
Many Body ◽  
Bifurcation Mechanism ◽  
Network Topologies ◽  
Many Body Systems ◽  
The Stability ◽  
Evolutionary Networks ◽  
Good Agreement

In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the microscopic quantum entanglement. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are invariant with a certain amount of microscopic entanglement, but they can be changed abruptly once the entanglement exceeds a critical value. Furthermore, we provide numerical evidence showing that the emergence of bifurcation is robust against the change of the network topologies, and the critical values are in good agreement with our theoretical prediction. These results show that the bifurcation mechanism could be ubiquitous in many physical systems, in addition to evolutionary networks.

scholarly journals Applications of fidelity measures to complex quantum systems

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150153 ◽  
Author(s):  
Sandro Wimberger
Keyword(s):  
Cold Atoms ◽  
Dimensional System ◽  
Many Body ◽  
Practical Applications ◽  
Dynamical Regimes ◽  
Many Body Systems ◽  
Fidelity Measures ◽  
The Stability ◽  
Low Dimensional ◽  
Quantum Motion

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular–chaotic phase space.

scholarly journals Landau–Zener Effect in Superfluid Nuclear Systems

2003 ◽  
Vol 18 (26) ◽  
pp. 1809-1817 ◽  
Author(s):  
M. Mirea
Keyword(s):  
Equations Of Motion ◽  
Deformation Energy ◽  
Cluster Decay ◽  
Many Body ◽  
Spectroscopic Factors ◽  
Nuclear Systems ◽  
Particle Level ◽  
Many Body Systems ◽  
Experimental Ratio ◽  
Good Agreement

The Landau–Zener effect is generalized for many-body systems with pairing residual interactions. The microscopic equations of motion are obtained and the 14C decay of 223Ra spectroscopic factors are deduced. An asymmetric nuclear shape parametrization given by two intersected spheres is used. The single particle level scheme is determined in the frame of the superasymmetric two-center shell model. The deformation energy is computed in the microscopic–macroscopic approximation. The penetrabilities are obtained within the WKB approximation. The fine structure of the cluster decay analyzed in the frame of this formalism gives a very good agreement with the experimental ratio of partial half-lives for transition to the first excited state and to the ground state.

scholarly journals Disorder in Quantum Many-Body Systems

2019 ◽  
Vol 10 (1) ◽  
pp. 233-252 ◽  
Author(s):  
Thomas Vojta
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Wave Functions ◽  
Many Body ◽  
Quantum Critical Points ◽  
Different Types ◽  
Many Body Systems ◽  
Random Disorder ◽  
The Stability ◽  
Ground State Phases

Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to prevent interesting new quantum states of matter from forming and to smear out sharp features associated with the phase transitions between them. However, disorder is also responsible for a variety of interesting novel phenomena that do not have clean counterparts. These include Anderson localization of single-particle wave functions, many-body localization in isolated many-body systems, exotic quantum critical points, and glassy ground-state phases. This brief review focuses on two separate but related subtopics in this field. First, we review under what conditions different types of randomness affect the stability of symmetry-broken low-temperature phases in quantum many-body systems and the stability of the corresponding phase transitions. Second, we discuss the fate of quantum phase transitions that are destabilized by disorder as well as the unconventional quantum Griffiths phases that emerge in their vicinity.

A NONEQUILIBRIUM STATISTICAL ENSEMBLE FORMALISM MaxEnt–NESOM: Basic Concepts, Construction, Application, Open Questions and Criticisms

2000 ◽  
Vol 14 (28) ◽  
pp. 3189-3264 ◽  
Author(s):  
ROBERTO LUZZI ◽  
ÁUREA R. VASCONCELLOS ◽  
J. GALVÃO RAMOS
Keyword(s):  
Function Theory ◽  
Operator Method ◽  
Statistical Thermodynamics ◽  
Statistical Ensemble ◽  
Many Body ◽  
Open Questions ◽  
Nonlinear Quantum ◽  
Many Body Systems ◽  
Ensemble Formalism ◽  
Good Agreement

We describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body systems. This is the so-called Nonequilibrium Statistical Operator Method, based on the seminal and fundamental ideas set forward by Boltzmann and Gibbs. The existing approaches can be unified under a unique variational principle, namely, MaxEnt, which we consider here. The main six basic steps that are at the foundations of the formalism are presented and the fundamental concepts are discussed. The associated nonlinear quantum kinetic theory and the accompanying Statistical Thermodynamics (the Informational Statistical Thermodynamics) are very briefly described. The corresponding response function theory for systems away from equilibrium allows to connected the theory with experiments, and some examples are summarized; there follows a good agreement between theory and experimental data in the cases in which the latter are presently available. We also present an overview of some conceptual questions and associated criticisms.

scholarly journals DENSITY FUNCTIONAL FOR PAIRING WITH PARTICLE NUMBER CONSERVATION

2010 ◽  
Vol 25 (21n23) ◽  
pp. 1854-1857
Author(s):  
DENIS LACROIX ◽  
GUILLAUME HUPIN
Keyword(s):  
Density Functional ◽  
Particle Number ◽  
Many Body ◽  
New Approach ◽  
Occupation Numbers ◽  
Particle Number Conservation ◽  
Coupling Strengths ◽  
Pairing Correlations ◽  
Many Body Systems ◽  
Good Agreement

In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.

The stability of many-body systems

2007 ◽  
Vol 19 (41) ◽  
pp. 416101 ◽  
Author(s):  
D M Heyes ◽  
G Rickayzen
Keyword(s):  
Many Body ◽  
Many Body Systems ◽  
The Stability

scholarly journals Hole probability for non-interacting fermions in a d-dimensional trap

2022 ◽  
Author(s):  
G. Gouraud ◽  
Pierre Le Doussal ◽  
Gregory Schehr
Keyword(s):  
Large Deviation ◽  
Fermi Gas ◽  
Exact Formula ◽  
Many Body ◽  
Large N ◽  
Fermi Wave Vector ◽  
Hole Probability ◽  
Many Body Systems ◽  
Universal Scaling Function ◽  
Good Agreement

Abstract The hole probability, i.e., the probability that a region is void of particles, is a benchmark of correlations in many body systems. We compute analytically this probability P (R) for a sphere of radius R in the case of N noninteracting fermions in their ground state in a d-dimensional trapping potential. Using a connection to the Laguerre-Wishart ensembles of random matrices, we show that, for large N and in the bulk of the Fermi gas, P (R) is described by a universal scaling function of kF R, for which we obtain an exact formula (kF being the local Fermi wave-vector). It exhibits a super exponential tail P (R) / e-κd(kF R)d+1 where κdis a universal amplitude, in good agreement with existing numerical simulations. When R is of the order of the radius of the Fermi gas, the hole probability is described by a large deviation form which is not universal and which we compute exactly for the harmonic potential. Similar results also hold in momentum space.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems
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