Hubbard-Stratonovich-like Transformations for Few-Body Interactions

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the an-alytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three-and more-body inter-actions, is presented.

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Many-body Green functions in nuclear physics

International Journal of Modern Physics E ◽

10.1142/s0218301317400250 ◽

2017 ◽

Vol 26 (01n02) ◽

pp. 1740025 ◽

Cited By ~ 1

Author(s):

J. Speth ◽

N. Lyutorovich

Keyword(s):

Nuclear Physics ◽

Green Functions ◽

Many Body ◽

General Applicability ◽

Pair Correlations ◽

Self Consistent ◽

The Many ◽

The One ◽

General Relations ◽

Three Body

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

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Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽

10.22331/q-2021-06-29-486 ◽

2021 ◽

Vol 5 ◽

pp. 486

Author(s):

Thomás Fogarty ◽

Miguel Ángel García-March ◽

Lea F. Santos ◽

Nathan L. Harshman

Keyword(s):

Quantum Chaos ◽

Cold Atoms ◽

Quantum Systems ◽

Particle Interactions ◽

Body System ◽

Many Body ◽

One Dimensional ◽

The Core ◽

Emergence Of Chaos ◽

Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

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On the generalized Brillouin-Wigner perturbation theory and the many-body problem

Advances in Quantum Chemistry - New Perspectives in Quantum Systems in Chemistry and Physics, Part 1 ◽

10.1016/s0065-3276(05)39013-7 ◽

2001 ◽

pp. 209-223 ◽

Cited By ~ 8

Author(s):

I. Hubač ◽

S. Wilson

Keyword(s):

Perturbation Theory ◽

Body Problem ◽

Many Body ◽

The Many

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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 ◽

10.3390/e22121342 ◽

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.

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Electronic Structure Calculations: The Many-Body Perturbation Theory (MBPT)

Introduction to Graphene-Based Nanomaterials ◽

10.1017/9781108664462.014 ◽

2020 ◽

pp. 373-378

Keyword(s):

Perturbation Theory ◽

Electronic Structure ◽

Electronic Structure Calculations ◽

Many Body ◽

Many Body Perturbation Theory ◽

The Many ◽

Structure Calculations

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Resonant and non-resonant contributions of B → K∗(p1,𝜖1){Kπ,ππ,KK} decay modes

Modern Physics Letters A ◽

10.1142/s0217732319500433 ◽

2019 ◽

Vol 34 (06) ◽

pp. 1950043

Author(s):

Mahboobeh Sayahi

Keyword(s):

Experimental Data ◽

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Branching Ratio ◽

Heavy Meson ◽

Chiral Perturbation ◽

Decay Modes ◽

Qcd Factorization ◽

Three Body ◽

Good Agreement

In this paper, the non-leptonic three-body decays [Formula: see text], [Formula: see text], [Formula: see text] are studied by introducing two-meson distribution amplitude for the [Formula: see text], [Formula: see text] and [Formula: see text] pairs in naive and QCD factorization (QCDF) approaches, such that the analysis is simplified into quasi-two body decays. By considering that the vector meson is being ejected in factorization, the resonant and non-resonant contributions are analyzed by using intermediate mesons in Breit–Wigner resonance formalism and the heavy meson chiral perturbation theory (HMChPT), respectively. The calculated values of the resonant and non-resonant branching ratio of [Formula: see text], [Formula: see text] and [Formula: see text] decay modes are compared with the experimental data. For [Formula: see text] and [Formula: see text], the non-resonant contributions are about 70–80% of experimental data, for which the total results by considering resonant contributions are in good agreement with the experiment.

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