相关论文: Explicit Equilibrium Solutions For the Aggregation…

We develop a field theory formalism for the disordered interacting electron liquid in the dynamical Keldysh formulation. This formalism is an alternative to the previously used replica technique. In addition it naturally allows for the…

Energy system optimization models are becoming increasingly popular for analyzing energy markets, such as the impact of new policies or interactions between energy carriers. One key challenge of these models is the trade-off between…

We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed…

Explicit solutions are obtained for a class of semilinear radial Schrodinger equations with power nonlinearities in multi-dimensions. These solutions include new similarity solutions and other new group-invariant solutions, as well as new…

We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…

In analogy to what happens in finite dimensions we state the Normal Form Theorem for k-singularities, introduced in the previous paper of the series. By means of that we study the local behaviour near a singularity i.e. we deduce local…

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…

We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a…

We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials $x^N$ ($N$ even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the…

We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…

In this paper we prove global existence of weak solutions, their regularization, and relaxation for large data for a broad class of Fokker-Planck-Alignment models which appear in collective dynamics. The main feature of these results, as…

We consider three classes of linear non-symmetric Fokker-Planck equations having a unique steady state and establish exponential convergence of solutions towards the steady state with explicit (estimates of) decay rates. First,…

Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…

In this paper, we address the existence of Fredholm backstepping transformations for self-adjoint and skew-adjoint operators $A$. Under suitable assumptions on the operator $A$ and the possibly unbounded control operator $B$, we prove the…

We construct a unified analytic framework connecting Bernoulli numbers, zeta-regularization, and Fredholm determinants associated with trigonometric selector kernels. Starting from the Bernoulli-Stirling algebra, Euler-Maclaurin corrections…

We analyze a numerical method for computing Fredholm determinants of trace class and Hilbert Schmidt integral operators defined in terms of matrix-valued kernels on the entire real line. With this method, the Fredholm determinant is…

We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in the number of particles) exponential convergence to…

We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in…

We present a generalized Ernst-type framework for stationary, axisymmetric spacetimes in which a scalar field is coupled to the electrodynamic field, with a particular focus on the ModMax theory. Our approach relies on the Weyl…

This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus…