Related papers: General criterion for harmonicity
We prove a version of the completeness hypothesis that follows from the coexistence of symmetry and gravity: tree-level gravitational scattering mandates single-particle states in all possible irreducible representations of the symmetry…
A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law…
Non-equilibrium path integral methods for computing quantum free energy differences are applied to a quantum particle trapped in a harmonic well of uniformly changing strength with the purpose of establishing the convergence properties of…
Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these…
We obtain an exact formula for the equilibrium free energy of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a heat bath of independent quantum harmonic…
The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In $\beta$-equilibrated matter, these two possibilities correspond to the Maxwell and…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
We prove that a wide class of models of Markov neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotide substitutions recently introduced and studied empirically by molecular…
According to maximum entropy principle, it has been proved that the gravitational field equations could be derived by the extrema of total entropy for perfect fluid, which implies that thermodynamic relations contain information of gravity.…
We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian…
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…
The fluctuations in the ideal quantum gases are studied using the strongly intensive measures $\Delta[A,B]$ and $\Sigma[A,B]$ defined in terms of two extensive quantities $A$ and $B$. In the present paper, these extensive quantities are…
We consider large non-Hermitian $N\times N$ matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance $1/N$ completely thermalises the bulk…
We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose,…
By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction…
A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite…
We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say $r$,…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
For a quantum system, a density matrix rho that is not pure can arise, via averaging, from a distribution mu of its wave function, a normalized vector belonging to its Hilbert space H. While rho itself does not determine a unique mu,…
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…