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The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of…

In this work, we present a complete characterization of the covariance structure of number statistics in boxes for hyperuniform point processes. Under a standard integrability assumption, the covariance depends solely on the overlap of the…

In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the…

Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…

In this short article we show how the techniques presented in arXiv:1207.4469 can be extended to a variety of non continuous and multivariate processes. As examples, we prove uniqueness of the location of the maximum for spectrally positive…

The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…

The constraints of the superfield method in two-dimensional supergravity are adapted to allow for nonvanishing bosonic torsion. As the analysis of the Bianchi identities reveals, a new vector superfield is encountered besides the well-known…

The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address…

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

Let $\eta_t$ be a Poisson point process with intensity measure $t\mu$, $t>0$, over a Borel space $\mathbb{X}$, where $\mu$ is a fixed measure. Another point process $\xi_t$ on the real line is constructed by applying a symmetric function…

We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…

Stochastic port-Hamiltonian systems on infinite-dimensional spaces governed by It\^o stochastic differential equations (SDEs) are introduced and some properties of this new class of systems are studied. They are an extension of stochastic…

It is shown that the quaternionic Hilbert space formulation of quantum mechanics allows a quantization, based on a generalized system of imprimitivity, that leads to a description of the motion of a quantum particle in the field of a…

In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…

In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by the asymptotic behavior of the widths of compact subsets with…

Using the Hubbard Hamiltonian for transition metal-3d and oxygen-2p states with perovskite geometry, we propose a new scaling procedure for a nontrivial extension of these systems to large spatial dimensions $D$. The scaling procedure is…

This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a L\'{e}vy driven stochastic differential equation whose coefficients are…

We study visibility from a fixed point in the presence of a Poisson process of $\lambda$--geodesic hyperplanes in a $d$-dimensional hyperbolic space. The family of $\lambda$--geodesic hyperplanes interpolates between totally geodesic…

It is shown by constructing Rohlins canonical measures that for a strictly stationary, d-dimensional vector-valued process X there exists another strictly stationary d-dimensional process U with uniform one-dimensional marginals and with…

We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…