Mean-field approximations to the many-body S-matrix

1981 ◽  
pp. 1-7
Author(s):  
S.E. Koonin ◽  
Y. Alhassid ◽  
K. R. Sandhya-Devi ◽  
W. K. Kellogg
Keyword(s):  
Mean Field ◽  
Many Body ◽  
S Matrix ◽  
The Many ◽  
Mean Field Approximations

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.

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

2011 ◽  
Vol 20 (02) ◽  
pp. 252-258 ◽  
Author(s):  
LUDOVIC BONNEAU ◽  
JULIEN LE BLOAS ◽  
PHILIPPE QUENTIN ◽  
NIKOLAY MINKOV
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Energy Difference ◽  
Pair Type ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
The Many ◽  
The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

Non-analyticity of the S-matrix in the many-body theory

1971 ◽  
Vol 34 (7) ◽  
pp. 374
Author(s):  
M. Binder ◽  
M. Razavy
Keyword(s):  
Many Body ◽  
Many Body Theory ◽  
S Matrix ◽  
The Many ◽  
Body Theory

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.

EXACT MANY BODY FERMI-BOSE TRANSMUTATION IN 2+1 DIMENSIONS

1992 ◽  
Vol 06 (22) ◽  
pp. 3543-3553
Author(s):  
D.M. GAITONDE ◽  
SUMATHI RAO
Keyword(s):  
Gauge Field ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Mean Field ◽  
Scalar Interaction ◽  
Many Body ◽  
Ground State Wavefunction ◽  
The Many ◽  
Chern Simons

We show that the low energy limit of relativistic fermions interacting with a statistical gauge field also includes a scalar interaction. When the Chern-Simons (CS) parameter µ=e2/2π and the scalar interaction is precisely that which is obtained through relativistic reduction, the many-body Hamiltonian can be solved exactly, directly in the fermion gauge, for the ground state energy which is zero and the ground state wavefunction which is gauge equivalent to one, characteristic of free bosons. Conversely, for N bosons interacting with a CS gauge field with µ=e2/2π, the mean-field ground state energy is πN2/m, which is characteristic of N free fermions.

scholarly journals Time-dependent mean-field approximations for many-body observables

1983 ◽  
Vol 28 (4) ◽  
pp. 1465-1474 ◽  
Author(s):  
T. Troudet ◽  
S. E. Koonin
Keyword(s):  
Mean Field ◽  
Time Dependent ◽  
Many Body ◽  
Mean Field Approximations

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.

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