Related papers: Remote temperature sensing in 2D and the Bergman k…
We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.
We investigate the radiation of energy and angular momentum from 2D topological systems with broken inversion symmetry and time reversal symmetry. A general theory of far-field radiation is developed using the linear response of 2D…
We address estimation of temperature for finite quantum systems at thermal equilibrium and show that the Landau bound to precision $\delta T^2 \propto T^2$, originally derived for a classical {\em not too small} system being a portion of a…
The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random and external field strength. Thermal states and thermodynamic properties are obtained for all…
We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a…
We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat…
Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…
This manuscript investigates the following aspects of the one dimensional dissipative Boltzmann equation associated to variable hard-spheres kernel: (1) we show the optimal cooling rate of the model by a careful study of the system…
Solving the time-dependent quantum many-body Schr\"odinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to…
A general expression for the temperature of a finite-dimensional quantum system is deduced from thermodynamic arguments. At equilibrium, this magnitude coincides with the standard thermodynamic temperature. Furthermore, it is well-defined…
In this paper, we study sharp two-sided heat kernel estimates for a large class of symmetric reflected diffusions with jumps on the closure of an inner uniform domain $D$ in a length metric space. The length metric is the intrinsic metric…
This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
We analyse the transverse dynamical two-point correlation function of the XX chain by means of a thermal form factor series. The series is rewritten in terms of the resolvent and the Fredholm determinant of an integrable integral operator.…
We consider the concept of temperature in a setting beyond the standard thermodynamics prescriptions. Namely, rather than restricting to standard coarse-grained measurements, we consider observers able to master any possible quantum…
The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…
We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the…
In this paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of…
In this paper, we derive sharp two side heat kernel estimate on exterior $C^{1,1}$ domains in the plane, and sharp upper heat kernel bound on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Estimates for Green's function…
In this work we investigate the heat kernel of the Laplace--Beltrami operator on a rectangular torus and the according temperature distribution. We compute the minimum and the maximum of the temperature on rectangular tori of fixed area by…