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.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

MEMORIAL TRIBUTE TO MANFRED L. RISTIG (1935–2011)

2013 ◽  
Vol 27 (29) ◽  
pp. 1347003
Author(s):  
JOHN W. CLARK
Keyword(s):  
Matrix Theory ◽  
Microscopic Theory ◽  
Quantum Fluids ◽  
Strong Interactions ◽  
Many Body ◽  
Exchange Effects ◽  
Nuclear Systems ◽  
Hypernetted Chain ◽  
Many Body Systems ◽  
Density Matrix Theory

Manfred Ristig was a leading contributor to the advancement of microscopic theory of strongly interacting quantum many-body systems for over four decades. This retrospective on his life and scientific career pays tribute to his pivotal role in the development of correlated wavefunction approaches to quantitative ab initio description of quantum fluids, nuclear systems and condensed matter more generally. Highlights include his contributions to the formulation of Fermi hypernetted chain theory and correlated density matrix theory. Special attention is given to Ristig's seminal work of recent years, which has yielded rich insights into the interplay of exchange effects (arising from quantum statistics) and the strong interactions between constituent bosons or fermions.

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 Time-delay polaritonics

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
J. D. Töpfer ◽  
H. Sigurdsson ◽  
L. Pickup ◽  
P. G. Lagoudakis
Keyword(s):  
Equations Of Motion ◽  
Signal Propagation ◽  
Matter Wave ◽  
Many Body ◽  
Coupled Equations ◽  
Exciton Polaritons ◽  
Non Linear ◽  
Linear Effects ◽  
Many Body Systems ◽  
Condensate System

AbstractNon-linearity and finite signal propagation speeds are omnipresent in nature, technologies, and real-world problems, where efficient ways of describing and predicting the effects of these elements are in high demand. Advances in engineering condensed matter systems, such as lattices of trapped condensates, have enabled studies on non-linear effects in many-body systems where exchange of particles between lattice nodes is effectively instantaneous. Here, we demonstrate a regime of macroscopic matter-wave systems, in which ballistically expanding condensates of microcavity exciton-polaritons act as picosecond, microscale non-linear oscillators subject to time-delayed interaction. The ease of optical control and readout of polariton condensates enables us to explore the phase space of two interacting condensates up to macroscopic distances highlighting its potential in extended configurations. We demonstrate deterministic tuning of the coupled-condensate system between fixed point and limit cycle regimes, which is fully reproduced by time-delayed coupled equations of motion similar to the Lang-Kobayashi equation.

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.

A Derivation of Relativistically-Invariant Nonlinear Field Equations for Strongly Interacting Many-Body Systems

1997 ◽  
Vol 11 (07) ◽  
pp. 929-944 ◽  
Author(s):  
J. A. Tuszyński ◽  
J. M. Dixon
Keyword(s):  
Field Equation ◽  
Equations Of Motion ◽  
Nonlinear Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Relativistic Regime ◽  
Klein Gordon ◽  
Many Body Systems ◽  
Nonlinear Field Equations

We re-examine the derivation of nonlinear field equations for a system of strongly interacting quasiparticles. Emphasis is placed on typical dispersion relations in the relativistic regime. Through Heisenberg's equations of motion for second-quantised operators we demonstrate that interacting many-body systems are described by a nonlinear Klein–Gordon type field equation. Its nonrelativistic equivalent was previously shown to be of the nonlinear Schrödinger type.

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 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.

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