Related papers: Strong uniqueness for Dirichlet operators related …
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
Quantum electrodynamics lies at the heart of hybrid quantum systems essential for future technologies. The thermodynamic limit of the Dicke model, a fundamental model describing these systems, predicts exotic quantum phenomena, such as…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
We describe a new method to bound certain higher-dimensional exponential sums which are associated with tori in symplectic groups over finite fields. Our method is based on the self-reducibility property of the Weil representation. As a…
We consider the stochastic 2-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique…
We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution…
We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…
We establish necessary and sufficient conditions for stochastic invariance of closed subsets in Hilbert spaces for solutions to infinite-dimensional stochastic differential equations (SDEs) under mild assumptions on the coefficients. Our…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We introduce an unrolled quantization $U_q^E(\mathfrak{gl}(1 \vert 1))$ of the complex Lie superalgebra $\mathfrak{gl}(1 \vert 1)$ and use its categories of weight modules to construct and study new three dimensional non-semisimple…
The connections between standard theoretical tools used to study open quantum systems can sometimes seem opaque. Whether it is a Lindblad master equation, the equation of motion for the Wigner function or a dissipative Keldysh action,…
In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
The Sine-Gordon - equivalently, the massive Thirring - Hamiltonian is ubiquitous in low-dimensional physics, with applications that range from cold atom and strongly correlated systems to quantum impurities. We study here its…
We develop a new method for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment. We find several new models with interesting features, such as…
We study the Dubrovin equation of the infinite-dimensional 2D Toda Dubrovin-Frobenius manifold at its irregular singularity. We first revisit the definition of the canonical coordinates, proving that they emerge naturally as generalized…
In a previous publication [J. Chem. Phys., 161, 044105 (2024)], it has been shown that Rothe's method can be used to solve the time-dependent Schr\"odinger equation (TDSE) for the hydrogen atom in a strong laser field using time-dependent…
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir…
The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can…
A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…