Related papers: Approximate scale invariance in particle systems: …
Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the…
A recently developed quasi two-dimensional exact-exchange formalism within the framework of Density Functional Theory has been applied to a strongly inhomogeneous interacting electron gas, and the results were compared with state-of-the-art…
We consider a quantum system of fixed size consisting of a regular chain of $n$-level subsystems, where $n$ is finite. Forming groups of $N$ subsystems each, we show that the strength of interaction between the groups scales with $N^{-…
At temperatures well below their glass transition, the deformation properties of bulk metallic glasses are characterised by a sharp transition from elasticity to plasticity, a reproducible yield stress, and an approximately linear decrease…
Amorphous solids exhibit intrinsic, local structural transitions, that give rise to the well known quantum-mechanical two-level systems at low temperatures. We explain the microscopic origin of the electric dipole moment of these two-level…
The crucial problem for better understanding the nature of glass transition and related relaxation phenomena is to find proper interrelations between molecular dynamics and thermodynamics of viscous systems. To gain this aim the recently…
We proved that the uncertainty relation fits in with many-particle system and the equality of the relation corresponds to the thermodynamic equilibrium state, the inequality of the relation corresponds to the thermodynamic non-equilibrium…
Recently extended precise numerical methods and droplet scaling arguments allow for a coherent picture of the glassy states of two-dimensional Ising spin glasses to be assembled. The length scale at which entropy becomes important and…
We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant…
It has been hypothesized that liquid polyamorphism, the existence of multiple amorphous states in a single component substance, may be caused by molecular or supramolecular interconversion. A simple microscopic model [Caupin and Anisimov,…
The phase behavior of hard-sphere particles interacting with a short-ranged potential is studied in the limit of infinite space dimensionality via the Franz-Parisi approach and the replica method of disordered systems. For an attractive…
Glasses feature a broad distribution of relaxation times and activation energies without an obvious characteristic scale. At the same time, macroscopic quantities such as Newtonian viscosity and nonlinear plastic deformation, are…
Low temperature properties of glasses are derived within a generalized tunneling model, considering the motion of charged particles on a closed path in a double-well potential. The presence of a magnetic induction field B violates the time…
So-called polar liquid crystals possess spontaneous long-range mutual orientation of their electric dipole moments, conferring bulk polarity to fluid phases of matter. The combination of polarity and fluidity leads to complex phase…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space…
Computer simulations recently revealed that several liquids exhibit strong correlations between virial and potential energy equilibrium fluctuations in the NVT ensemble [U. R. Pedersen {\it et al.}, Phys. Rev. Lett. {\bf 100}, 015701…
Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential…