Level curvatures, spectral statistics and scaling for interacting particles

The solvation effect of a number of nonaqueous polar solvents was studied on the oxidation-reduction properties of the [Co(en)3]3+-[Co(en)3]2+ system. Interactions of these ions with the solvent molecules are discussed in terms of their coordination, which is accompanied by a specific interaction of the Lewis acid-base type, namely formation of a hydrogen bond between the interacting particles. This is the main controlling factor of the redox properties of the studied system.

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Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0028 ◽

2020 ◽

Vol 75 (5) ◽

pp. 449-463

Author(s):

Dominik Lips ◽

Artem Ryabov ◽

Philipp Maass

Keyword(s):

Current Density ◽

Lattice Gas ◽

Yukawa Potential ◽

Exclusion Process ◽

Quantum Spin ◽

Nonequilibrium Steady States ◽

Interacting Particles ◽

Driven Diffusive Systems ◽

Periodic Potentials ◽

Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

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A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/prm.2020.49 ◽

2020 ◽

pp. 1-35

Author(s):

Benjamin D. Goddard ◽

Tim D. Hurst ◽

Mark Wilkinson

Keyword(s):

Liouville Equation ◽

Particle Dynamics ◽

Fundamental Importance ◽

Continuum Models ◽

Hard Particle ◽

Interacting Particles ◽

Weak Formulation ◽

Physical Systems ◽

Physical Particle

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using two examples.

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CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data

Statistical Papers ◽

10.1007/s00362-021-01250-3 ◽

2021 ◽

Author(s):

Tingting Zou ◽

Shurong Zheng ◽

Zhidong Bai ◽

Jianfeng Yao ◽

Hongtu Zhu

Keyword(s):

Covariance Matrices ◽

Dependent Data ◽

Sample Covariance Matrices ◽

Sample Covariance ◽

Spectral Statistics

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Chaos on the hypercube

Journal of High Energy Physics ◽

10.1007/jhep11(2020)154 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Yiyang Jia ◽

Jacobus J. M. Verbaarschot

Keyword(s):

Magnetic Flux ◽

Spectral Density ◽

Hermite Polynomials ◽

Weighted Sums ◽

Majorana Fermions ◽

Chord Diagrams ◽

Magnetic Inversion ◽

Constant Magnitude ◽

Kitaev Model ◽

Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

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