相关论文: Loewner's Differential Equation and Spidernets

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…

We describe some analogues of quantum potentials arising in fractional or deformed Schroedinger equations.

We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…

In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear…

In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…

The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted to finite graphs, as a particular instance of Morse-Witten…

Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position…

The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap…

The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct…

We investigate the Lawson genus $2$ surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a $4-$punctured sphere. We describe the symmetries of…

We present a proof of a multidimensional version of Peres-Schlag's theorem on Diophantine approximations with lacunary sequences.

Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…

Our goal is to finally settle the persistent problem in Diophantine Approximation of finding best linear approximates. Classical results from the theory of continued fractions provide the solution for the special homogeneous case in the…

Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on…

A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be…

The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that…

A large system of ordinary differential equations is approximated by a parabolic partial differential equation with dynamic boundary condition and a different one with Robin boundary condition. Using the theory of differential operators…

The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions…

This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single…

The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the…