Related papers: A Lower Bound on the Partition Function for a Stri…
Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side $L\geq 1$ and subjected to a constant magnetic field $B\neq 0$. If the bulk density of particles $\rho$ and the temperature $T$ are…
We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and…
Some time ago we have suggested that positive vacuum energy exhibits a finite quantum break time, which can be a signal that a positive cosmological constant is inconsistent. From the requirement that Universe never undergoes through…
Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles.…
In this paper we analyze again a transition from the classical to quantum description of bound charged particles, which involves a substantial modification of the structure of their electromagnetic (EM) fields related to the well-known fact…
We study static, spherically symmetric, self-gravitating systems minimally coupled to a scalar field with U(1) gauge symmetry: charged boson stars. We find numerical solutions to the EinsteinMaxwell equations coupled to the relativistic…
We prove an upper bound on the excess charge for non-relativistic atomic systems, independent of the particle statistics. This result improves Lieb's bound of 1984 for any $Z \ge 12$.
The particle number and energy fluctuations in the system of charged particles are studied in the canonical ensemble for non-zero net values of the conserved charge. In the thermodynamic limit the fluctuations in the canonical ensemble are…
We study the electric potential and field produced by disordered distributions of charge to see why clumps of charge do not produce large potentials or fields. The question is answered by evaluating the probability distribution of the…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
We consider finite harmonic chain (consisting of N classical particles) plus dissipative force acting on one particle (called dissipating particle) only. We want to prove that "in the generic case" the energy (per particle) for the whole…
Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field $B$ perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal…
The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an…
A lower bound is derived for the boundary entropy s = ln g of a 1+1d quantum critical system with boundary, under the conditions that the bulk conformal central charge c is >=1 and the most relevant bulk scaling dimension is >(c-1)/12. This…
Fixing the number of particles $N$, the quantum canonical ensemble imposes a constraint on the occupation numbers of single-particle states. The constraint particularly hampers the systematic calculation of the partition function and any…
The free scalar field is studied on the Y-junction of three semi infinite axes which is the simplest example of a non-manifold space. It is shown that under an assumption that the junction point can not gain a macroscopic amount of energy…
Past studies of fractional quantum Hall systems have found that the charge gap dominates the neutral gap for all relevant parameter choices. We report a wide-ranging proof that this domination is in fact a universal property of any…
The exact canonical partition function of a hard disk system in a narrow quasi-one dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result the many body problem is reduced to solving two…
In this note, we first try to prove a uniform lower bound of nodal volume in elliptic homogenization setting. This lower bound is far from optimal. But, we can prove a constant lower bound in dimension two. Motivated by the proof, we extend…