Special Issue "Various Routes towards Few-Body Physics"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 June 2021.

Special Issue Editors

Prof. Dr. Tomasz Sowiński
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Guest Editor
Few-Body Problems Theory GroupInstitute of Physics, Polish Academy of SciencesAleja Lotnikow 32/46, PL-02668 Warsaw, Poland
Interests: ultra-cold atoms; strongly correlated quantum systems; optical lattices
Dr. Miguel Ángel García-March
Website
Guest Editor
ICFO – The Institute of Photonic Sciences, Av. C.F. Gauss 3, SP-08860 Castelldefels, Barcelona, Spain
Interests: ultra-cold atoms; open classical and quantum systems; complex quantum dynamics; strongly correlated quantum systems; anomalous diffusion in complex classical environments; few-atom systems; nonlinear and singular optics; quantum simulators and sensors; quantum thermodynamics and relaxation in closed quantum systems

Special Issue Information

Dear Colleagues,

Physical systems containing a mesoscopic number of particles form a general and natural bridge between single-particle problems and many-body physics. Therefore, a better understanding of properties of such systems and their scalability has fundamental importance in different areas of physics. Natural universality of the few-body systems is, however, not well exploited, and physicists working on seemingly different problems do not always take advantage of successive progress in the whole field. One of the natural connections between different mesoscopic systems arises from the fact that all few-body systems are very elusive for standard analytical and computational techniques, i.e., these systems are too complicated for straightforward analytical or quasi-analytical treatments, and at the same time, they are too small if many-body methods are considered. Therefore, developments of theoretical and experimental techniques dedicated to these systems should be broadly promoted.

The purpose of this Special Issue is to open another platform for scientific discussions and exchange different ideas related to few-body systems. We welcome contributions from all areas of physics where classical or quantum systems of several particles are considered. The Issue is open not only to theoretical as well as experimental works dedicated to ideas, methods, and techniques building our understanding of few-body systems but also for papers where different interesting properties of such systems are studied and discussed. In this issue, we would also like to promote the idea that well-controlled few-atom systems may serve as quantum simulators for different few-body problems and help to explore spectacular consequences of a collective behavior originating in interparticle interactions and quantum statistics. Therefore, we invite everyone having scientific interests in atomic and molecular physics, condensed and soft matter physics, nuclear and particle physics, stellar and astrophysics, or computational and mathematical physics to contribute with papers focusing on few-body problems.

Prof. Dr. Tomasz Sowiński
Dr. Miguel A. Garcia-March
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Classical and quantum few-body systems
  • Correlations induced by interactions and statistics
  • ‘Few’ to ‘Many’ crossover
  • Mesoscopic physics

Published Papers (3 papers)

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Research

Open AccessArticle
Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential
Mathematics 2020, 8(7), 1196; https://doi.org/10.3390/math8071196 - 21 Jul 2020
Abstract
We provide a detailed study of the properties of a few interacting spin 1/2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of [...] Read more.
We provide a detailed study of the properties of a few interacting spin 1 / 2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The N = 2 case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for N = 2 , 3 , 4 and 5 particles, e.g., low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength. Full article
(This article belongs to the Special Issue Various Routes towards Few-Body Physics)
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Open AccessArticle
The Dynamics of Digits: Calculating Pi with Galperin’s Billiards
Mathematics 2020, 8(4), 509; https://doi.org/10.3390/math8040509 - 02 Apr 2020
Abstract
In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π. This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio [...] Read more.
In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases. Full article
(This article belongs to the Special Issue Various Routes towards Few-Body Physics)
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Open AccessArticle
Clusters in Separated Tubes of Tilted Dipoles
Mathematics 2020, 8(4), 484; https://doi.org/10.3390/math8040484 - 01 Apr 2020
Abstract
A few-body cluster is a building block of a many-body system in a gas phase provided the temperature at most is of the order of the binding energy of this cluster. Here we illustrate this statement by considering a system of tubes filled [...] Read more.
A few-body cluster is a building block of a many-body system in a gas phase provided the temperature at most is of the order of the binding energy of this cluster. Here we illustrate this statement by considering a system of tubes filled with dipolar distinguishable particles. We calculate the partition function, which determines the probability to find a few-body cluster at a given temperature. The input for our calculations—the energies of few-body clusters—is estimated using the harmonic approximation. We first describe and demonstrate the validity of our numerical procedure. Then we discuss the results featuring melting of the zero-temperature many-body state into a gas of free particles and few-body clusters. For temperature higher than its binding energy threshold, the dimers overwhelmingly dominate the ensemble, where the remaining probability is in free particles. At very high temperatures free (harmonic oscillator trap-bound) particle dominance is eventually reached. This structure evolution appears both for one and two particles in each layer providing crucial information about the behavior of ultracold dipolar gases. The investigation addresses the transition region between few- and many-body physics as a function of temperature using a system of ten dipoles in five tubes. Full article
(This article belongs to the Special Issue Various Routes towards Few-Body Physics)
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