Yang–Yang equilibrium statistical mechanics: A brilliant method

2016 ◽  
Vol 30 (09) ◽  
pp. 1630008
Author(s):  
Xi-Wen Guan ◽  
Yang-Yang Chen
Keyword(s):  
Statistical Mechanics ◽  
Weak Interactions ◽  
Delta Function ◽  
Ideal Gas ◽  
Baxter Equation ◽  
Dimensional System ◽  
Equilibrium Statistical Mechanics ◽  
Rigorous Approach ◽  
Wide Range ◽  
The One

Yang and Yang in 1969 [J. Math. Phys. 10, 1115 (1969)] for the first time proposed a rigorous approach to the thermodynamics of the one-dimensional system of bosons with a delta-function interaction. This paper was a breakthrough in exact statistical mechanics, after Yang [Phys. Rev. Lett. 19, 1312 (1967)] published his seminal work on the discovery of the Yang–Baxter equation in 1967. Yang and Yang’s brilliant method yields significant applications in a wide range of fields of physics. In this paper, we briefly introduce the method of the Yang–Yang equilibrium statistical mechanics and demonstrate a fundamental application of the Yang–Yang method for the study of thermodynamics of the Lieb–Liniger model with strong and weak interactions in a whole temperature regime. We also consider the equivalence between the Yang–Yang’s thermodynamic Bethe ansatz equation and the thermodynamics of the ideal gas with the Haldane’s generalized exclusion statistics.

scholarly journals EQUILIBRIUM STATISTICAL MECHANICS OF FERMION LATTICE SYSTEMS

2003 ◽  
Vol 15 (02) ◽  
pp. 93-198 ◽  
Author(s):  
HUZIHIRO ARAKI ◽  
HAJIME MORIYA
Keyword(s):  
Statistical Mechanics ◽  
Interaction Energy ◽  
Convergence Condition ◽  
Point Interaction ◽  
Translation Invariance ◽  
Major Result ◽  
Lattice Systems ◽  
Equilibrium Statistical Mechanics ◽  
Spin Lattice ◽  
The One

We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the equivalence of the KMS condition and the variational principle with a minimal assumption for the dynamics and without any explicit assumption on the potential. Its proof applies to spin lattice systems as well, yielding a vast improvement over known results. All formulations are in terms of a C*-dynamical systems for the Fermion (CAR) algebra [Formula: see text] with all or a part of the following assumptions: (I) The interaction is even, namely, the dynamics αt commutes with the even-oddness automorphism Θ. (Automatically satisfied when (IV) is assumed.) (II) The domain of the generator δα of αt contains the set [Formula: see text] of all strictly local elements of [Formula: see text]. (III) The set [Formula: see text] is the core of δα. (IV) The dynamics αt commutes with lattice translation automorphism group τ of [Formula: see text]. A major technical tool is the conditional expectation from [Formula: see text] onto its C*-subalgebras [Formula: see text] for any subset I of the lattice, which induces a system of commuting squares. This technique overcomes the lack of tensor product structures for Fermion systems and even simplifies many known arguments for spin lattice systems. In particular, this tool is used for obtaining the isomorphism between the real vector space of all *-derivations with their domain [Formula: see text], commuting with Θ, and that of all Θ-even standard potentials which satisfy a specific norm convergence condition for the one point interaction energy. This makes it possible to associate a unique standard potential to every dynamics satisfying (I) and (II). The convergence condition for the potential is a consequence of its definition in terms of the *-derivation and not an additional assumption. If translation invariance is imposed on *-derivations and potentials, then the isomorphism is kept and the space of translation covariant standard potentials becomes a separable Banach space with respect to the norm of the one point interaction energy. This is a crucial basis for an application of convex analysis to the equivalence proof in the major result. Everything goes in parallel for spin lattice systems without the evenness assumption (I).

scholarly journals A Mach-sensitive splitting approach for Euler-like systems

2018 ◽  
Vol 52 (1) ◽  
pp. 207-253 ◽  
Author(s):  
D. Iampietro ◽  
F. Daude ◽  
P. Galon ◽  
J.-M. Hérard
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Ideal Gas ◽  
Present Approach ◽  
Type Method ◽  
One Dimensional ◽  
Wide Range ◽  
The One ◽  
Number Case ◽  
Acoustic Phenomenon

Herein, a Mach-sensitive fractional step approach is proposed for Euler-like systems. The key idea is to introduce a time-dependent splitting which dynamically decouples convection from acoustic phenomenon following the fluctuations of the flow Mach number. By doing so, one seeks to maintain the accuracy of the computed solution for all Mach number regimes. Indeed, when the Mach number takes high values, a time-explicit resolution of the overall Euler-like system is entirely performed in one of the present splitting step. On the contrary, in the low-Mach number case, convection is totally separated from the acoustic waves production. Then, by performing an appropriate correction on the acoustic step of the splitting, the numerical diffusion can be significantly reduced. A study made on both convective and acoustic subsystems of the present approach has revealed some key properties as hyperbolicity and positivity of the density and internal energy in the case of an ideal gas thermodynamics. The one-dimensional results made on a wide range of Mach numbers using an ideal and a stiffened gas thermodynamics show that the present approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.

scholarly journals Professor Chen Ping Yang’s early significant contributions to mathematical physics

2019 ◽  
Vol 33 (06) ◽  
pp. 1930002
Author(s):  
Xi-Wen Guan ◽  
Feng He
Keyword(s):  
Statistical Mechanics ◽  
Spin Chain ◽  
Lattice Gas ◽  
Quantum Statistical Mechanics ◽  
Delta Function ◽  
Mathematical Physics ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Wide Range ◽  
Chen Ning Yang

In the 60s Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe’s hypothesis for various problems of physics. The works on the lattice gas model, critical behavior in liquid–gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe’s hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.

Statistical Mechanics and Quantum Field Theory

2019 ◽  
pp. 177-187
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Dimensional System ◽  
Quantum Field ◽  
Single Degree Of Freedom ◽  
General Terms ◽  
The One

The connection between statistical mechanics on the one side and quantum mechanics and quantum field theory on the other side is based on the analogy between thermal and quantum fluctuations. Formally, the connection is expressed through the mathematical equivalence between the partition function in statistical mechanics and the propagator in quantum field theory. This chapter explores the equivalence between statistical mechanics and quantum mechanics or quantum field theory in general terms using the Feynman path integral and with the example of the equivalence between the classical XY Heisenberg model and the sigma model of quantum field theory. Invoking the concepts of the partition function and the transfer matrix, an example demonstrates the passage from the quantum mechanics of a single degree of freedom, a zero-dimensional system, to the statistical mechanics of a one-dimensional system represented by classical variables.

General Trend of Negative Transference Number in Li Salt/Ionic Liquid Mixtures

2019 ◽  
Author(s):  
Nicola Molinari ◽  
Jonathan P. Mailoa ◽  
Boris Kozinsky
Keyword(s):  
Ionic Liquid ◽  
Transference Number ◽  
Liquid Mixtures ◽  
Single Linkage ◽  
Self Diffusion ◽  
Wide Range ◽  
Single Linkage Cluster ◽  
Concentrated Solution ◽  
The One ◽  
Dynamics Simulations

We show that strong cation-anion interactions in a wide range of lithium-salt/ionic liquid mixtures result in a negative lithium transference number, using molecular dynamics simulations and rigorous concentrated solution theory. This behavior fundamentally deviates from the one obtained using self-diffusion coefficient analysis and agrees well with experimental electrophoretic NMR measurements, which accounts for ion correlations. We extend these findings to several ionic liquid compositions. We investigate the degree of spatial ionic coordination employing single-linkage cluster analysis, unveiling asymmetrical anion-cation clusters. Additionally, we formulate a way to compute the effective lithium charge that corresponds to and agrees well with electrophoretic measurements and show that lithium effectively carries a negative charge in a remarkably wide range of chemistries and concentrations. The generality of our observation has significant implications for the energy storage community, emphasizing the need to reconsider the potential of these systems as next generation battery electrolytes.<br>

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals Modes of Interaction in Naturally Occurring Medical Encounters With General Practitioners: The “One in a Million” Study

2021 ◽  
pp. 104973232199379
Author(s):  
Olaug S. Lian ◽  
Sarah Nettleton ◽  
Åge Wifstad ◽  
Christopher Dowrick
Keyword(s):  
General Practitioners ◽  
Narrative Analysis ◽  
Mode Competition ◽  
General Applicability ◽  
Naturally Occurring ◽  
Wide Range ◽  
The One ◽  
Narrative Mode ◽  
Modes Of Interaction

In this article, we qualitatively explore the manner and style in which medical encounters between patients and general practitioners (GPs) are mutually conducted, as exhibited in situ in 10 consultations sourced from the One in a Million: Primary Care Consultations Archive in England. Our main objectives are to identify interactional modes, to develop a classification of these modes, and to uncover how modes emerge and shift both within and between consultations. Deploying an interactional perspective and a thematic and narrative analysis of consultation transcripts, we identified five distinctive interactional modes: question and answer (Q&A) mode, lecture mode, probabilistic mode, competition mode, and narrative mode. Most modes are GP-led. Mode shifts within consultations generally map on to the chronology of the medical encounter. Patient-led narrative modes are initiated by patients themselves, which demonstrates agency. Our classification of modes derives from complete naturally occurring consultations, covering a wide range of symptoms, and may have general applicability.

scholarly journals Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 290
Author(s):  
Maxim Pyzh ◽  
Kevin Keiler ◽  
Simeon I. Mistakidis ◽  
Peter Schmelcher
Keyword(s):  
Structural Changes ◽  
Many Body ◽  
Wide Range ◽  
Entropy Measures ◽  
Particle Level ◽  
The Many ◽  
The One ◽  
Tunneling Dynamics ◽  
The Individual ◽  
Trapped Bosons

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials.

scholarly journals Bio-Inspired Modality Fusion for Active Speaker Detection

2021 ◽  
Vol 11 (8) ◽  
pp. 3397
Author(s):  
Gustavo Assunção ◽  
Nuno Gonçalves ◽  
Paulo Menezes
Keyword(s):  
Superior Colliculus ◽  
Visual Information ◽  
Human Beings ◽  
Validation Process ◽  
Detection Approach ◽  
Wide Range ◽  
Speaker Detection ◽  
The One ◽  
The Brain ◽  
Fusion Ability

Human beings have developed fantastic abilities to integrate information from various sensory sources exploring their inherent complementarity. Perceptual capabilities are therefore heightened, enabling, for instance, the well-known "cocktail party" and McGurk effects, i.e., speech disambiguation from a panoply of sound signals. This fusion ability is also key in refining the perception of sound source location, as in distinguishing whose voice is being heard in a group conversation. Furthermore, neuroscience has successfully identified the superior colliculus region in the brain as the one responsible for this modality fusion, with a handful of biological models having been proposed to approach its underlying neurophysiological process. Deriving inspiration from one of these models, this paper presents a methodology for effectively fusing correlated auditory and visual information for active speaker detection. Such an ability can have a wide range of applications, from teleconferencing systems to social robotics. The detection approach initially routes auditory and visual information through two specialized neural network structures. The resulting embeddings are fused via a novel layer based on the superior colliculus, whose topological structure emulates spatial neuron cross-mapping of unimodal perceptual fields. The validation process employed two publicly available datasets, with achieved results confirming and greatly surpassing initial expectations.

Sign in / Sign up

Export Citation Format

Share Document