相关论文: Exact Solution of 1-matrix Model

We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…

We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…

We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schr\"odinger equation, from which expansions of the Green function can be obtained. Making use of the equivalent Fokker-Planck equation,…

A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a…

We show that the general solution of scalar field cosmology in $d$ dimensions with exponential potentials for flat Robertson-Walker metric can be found in a straightforward way by introducing new variables which completely decouple the…

We study the one-body reduced density matrix of a system of $N$ one-dimensional impenetrable anyons trapped by a harmonic potential. To this purpose we extend two methods developed to tackle related problems, namely the determinant approach…

We compute an the genus 1 correction to free energy of Hermitian two-matrix model in terms of theta-functions associated to spectral curve arising in large N limit. We discuss the relationship of this expression to isomonodromic…

We propose the relaxation bootstrap method for the numerical solution of multi-matrix models in the large $N$ limit, developing and improving the recent proposal of H.Lin. It gives rigorous inequalities on the single trace moments of the…

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…

The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this…

In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three…

We compute the high-dimensional limit of the free energy associated with a multi-layer generalized linear model. Under certain technical assumptions, we identify the limit in terms of a variational formula. The approach is to first show…

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to…

We prove a maximality theorem for one-parameter dynamical systems including multiplier one-parameter dynamical systems. Our main result is new even for one-parameter actions on commutative multiplier algebras including the algebra of…

We study the general problem of strengthening the logic of a given (partial) (non-deterministic) matrix with a set of axioms, using the idea of rexpansion. We obtain two characterization methods: a very general but not very effective one,…

We consider the numerical computation of finite-genus solutions of the Korteweg-de Vries equation when the genus is large. Our method applies both to the initial-value problem when spectral data can be computed and to dressing scenarios…

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally…

We consider excitations with the quantum numbers of a hole in the one dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in…

It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…