Related papers: From Brownian-time Brownian sheet to a fourth orde…
This note proves that the separation convergence towards the uniform distribution abruptly occurs at times around ln(n)/n for the (time-accelerated by 2) Brownian motion on the sphere with a high dimension n. The arguments are based on a…
As a result of the competition between self-propulsion and excluded volume interactions, purely repulsive self-propelled spherical particles undergo a motility-induced phase separation (MIPS). We carry out a systematic computational study,…
We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…
We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
We study the emergence of anticoncentration and approximate unitary design behavior in local Brownian circuits. The dynamics of circuit averaged moments of the probability distribution and entropies of the output state can be represented as…
We establish that the exact quantum dynamics of a Brownian particle in the Caldeira-Leggett model can be mapped, at any temperature, onto a classical, non-Markovian stochastic process in phase space. Starting from a correlated thermal…
We demonstrate that the well-known $(k\uparrow, -k\downarrow)$ Bardeen-Cooper-Schrieffer interaction, when considered in real space, is equivalent to an infinite-range Penson-Kolb pairing mechanism coexisting with an attractive Hubbard…
Consider a system of infinitely many Brownian particles on the real line. At any moment, these particles can be ranked from the bottom upward. Each particle moves as a Brownian motion with drift and diffusion coefficients depending on its…
We study the two-dimensional attractive Hubbard model using the mapping onto the half-filled repulsive Hubbard model in a uniform magnetic field coupled to the fermion spins. The low-energy effective action for charge and pairing…
We consider a diffusion in $\mathbb{R}^n$ whose coordinates each behave as one-dimensional Brownian motions, that behave independently when apart, but have a sticky interaction when they meet. The diffusion in $\mathbb{R}^n$ can be viewed…
Suspensions of Active Brownian Particles (ABP) undergo motility induced phase separation (MIPS) over a wide range of mean density and activity strength [1], even in the absence of an explicit attraction. Negative values of the mechanical…
Interacting many-particle systems with a mean-field one body part plus a chaos generating random two-body interaction having strength $\lambda$, exhibit Poisson to GOE and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and…
We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped…
Consider an n-fold integrated Brownian motion. We show that a simple change in time and scale transforms it into a stationary Gaussian process. The collection of stationary processes so constructed not only constitutes an interesting family…
The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the $nn$ pairing interaction is provided by a realistic bare $nn$ potential fitted to scattering data, it is…
Considering viscous friction that varies spatially and temporally, the general expressions for entropy production, free energy, and entropy extraction rates are derived to a Brownian particle that walks in an overdamped and underdamped…
We investigate a two-dimensional system of interacting Active Brownian Particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the…
The non-Hermitian matrix-valued Brownian motion is the stochastic process of a random matrix whose entries are given by independent complex Brownian motions. The bi-orthogonality relation is imposed between the right and the left…
Polymer rings in solution are either permanently entangled or not. Permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume. Conversely,…