scholarly journals A CORRELATION ESTIMATE FOR QUANTUM MANY-BODY SYSTEMS AT POSITIVE TEMPERATURE

2006 ◽  
Vol 18 (03) ◽  
pp. 233-253 ◽  
Author(s):  
ROBERT SEIRINGER
Keyword(s):  
Free Energy ◽  
Fock Space ◽  
Einstein Condensation ◽  
Positive Temperature ◽  
Coulomb Interactions ◽  
Many Body ◽  
Expectation Value ◽  
Many Body Systems ◽  
The Difference ◽  
Correlation Estimate

We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose–Einstein condensation.

scholarly journals Chaos in the Bose-Hubbard model and Random Two-Body Hamiltonians

2021 ◽  
Author(s):  
Lukas Pausch ◽  
Edoardo G Carnio ◽  
Andreas Buchleitner ◽  
Alberto Rodríguez González
Keyword(s):  
Hubbard Model ◽  
Fock Space ◽  
Fractal Dimensions ◽  
Chaotic Regime ◽  
Particle Interactions ◽  
Many Body ◽  
Expectation Value ◽  
Matrix Ensemble ◽  
Gaussian Orthogonal Ensemble ◽  
Many Body Systems

Abstract We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.

Symplectic Schrödinger equation for many-body systems

2020 ◽  
Vol 35 (06) ◽  
pp. 2050033
Author(s):  
R. G. G. Amorim ◽  
M. C. B. Fernandes ◽  
F. C. Khanna ◽  
A. E. Santana ◽  
J. D. M. Vianna
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Basic Element ◽  
Space Representation ◽  
Many Body ◽  
Many Body Systems ◽  
The Green Function ◽  
Phase Space Representation

Using elements of symmetry, as gauge invariance, many aspects of a Schrödinger equation in phase space are analyzed. The number (Fock space) representation is constructed in phase space and the Green function, directly associated with the Wigner function, is introduced as a basic element of perturbative procedure. This phase space representation is applied to the Landau problem and the Liouville potential.

Inequalities for the Energy and Free Energy of Many-Body Systems

1969 ◽  
Vol 22 (20) ◽  
pp. 1045-1047 ◽  
Author(s):  
Peter Kleban ◽  
R. V. Lange
Keyword(s):  
Free Energy ◽  
Many Body ◽  
Many Body Systems

Spin-Polarized Quantum Fluids and Solids

MRS Bulletin ◽  
1993 ◽  
Vol 18 (8) ◽  
pp. 38-43
Author(s):  
Kevin S. Bedell ◽  
Isaac F. Silvera ◽  
Neil S. Sullivan
Keyword(s):  
Magnetic Ordering ◽  
Quantum Fluids ◽  
Einstein Condensation ◽  
Many Body ◽  
Spin Polarized ◽  
Many Body Systems ◽  
The Rich ◽  
Bose Einstein ◽  
Physical Phenomena

The spin-polarized phases of the quantum fluids and solids, liquid 3He, solid 3He, and spin-aligned hydrogen have generated considerable excitement over the past fifteen years. The introduction of high magnetic fields (B ∼ 10–30 T) in conjunction with low temperatures (T ≲ 100 mK) has given rise to opportunities for exploring some of the new phases predicted for these materials. There is a broad range of physical phenomena that can be accessed in this regime of parameter space—unconventional superfluidity, unusual magnetic ordering, Bose-Einstein condensation and Kosterlitz-Thouless transitions, to name a few. This is most surprising since this plethora of complicated states of matter are present in some of the most uncomplicated materials. The rich variety of phases found in these materials are all examples of collective phenomena of quantum many-body systems, and they serve as prototypes for developing an understanding of magnetism and order/disorder processes in other systems, and for the design and characterization of new materials.

scholarly journals Cavity Volume and Free Energy in Many-Body Systems

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Jamie M. Taylor ◽  
Thomas G. Fai ◽  
Epifanio G. Virga ◽  
Xiaoyu Zheng ◽  
Peter Palffy-Muhoray
Keyword(s):  
Free Energy ◽  
Cavity Volume ◽  
Many Body ◽  
Many Body Systems

Inequalities for the Energy and Free Energy of Many-Body Systems

1969 ◽  
Vol 22 (25) ◽  
pp. 1413-1413
Author(s):  
Peter Kleban ◽  
R. V. Lange
Keyword(s):  
Free Energy ◽  
Many Body ◽  
Many Body Systems

scholarly journals Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory

2018 ◽  
Vol 115 (10) ◽  
pp. 2282-2286
Author(s):  
Lin Lin ◽  
Michael Lindsey
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Infinite Order ◽  
Many Body ◽  
Lattice Field Theory ◽  
Numerical Evidence ◽  
Lattice Field ◽  
Variational Structure ◽  
Euclidean Lattice ◽  
Many Body Systems

The Luttinger–Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green’s function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger–Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger–Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger–Ward functional, the free energy can be variationally minimized with respect to Green’s functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.

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