Related papers: Rest energy effects for non-relativistic Fermi fie…
We study the ground-state of a Fermi gas with short range attrative interactions in one or two dimensions. N fermions are placed in a confining potential, and interact with each other through a negative potential, whose range is larger than…
We explore the validity of the generalized Bekenstein bound, S <= pi M a. We define the entropy S as the logarithm of the number of states which have energy eigenvalue below M and are localized to a flat space region of width a. If boundary…
Upper and lower bounds are derived for the ground-state energy of neutral atoms which for $Z\to\infty$ both involve the limits of exact Green's functions with one-body potentials. The limits of both bounds are shown to coincide with the…
A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to…
Recently obtained results on linear energy bounds are generalized to arbitrary spin quantum numbers and coupling schemes. Thereby the class of so-called independent magnon states, for which the relative ground-state property can be…
The effects of a radiation field (RF) on the interaction process of a relativistic electron beam (REB) with an electron plasma are investigated. The stopping power of the test electron averaged with a period of the RF has been calculated…
The general structure of the $s$-wave fermionic superfluid pairing order parameter is discussed for systems in thermal equilibrium. We demonstrate that for finite-size systems with fixed boundary conditions the pairing-amplitude may always…
We extend the "gauge choice" problem Lamb noticed to include a time-dependent relativistic non-perturbative Coulomb field, which can be produced by a cluster of relativistic charged particles. If adiabatic conditions are carefully…
By definition, the exterior asymptotic energy of a solution to a wave equation on $\mathbb{R}^{1+N}$ is the sum of the limits as $t\to \pm\infty$ of the energy in the the exterior $\{|x|>|t|\}$ of the wave cone. In our previous work (JEMS…
We obtain new constraints for the modular energy of general states by using the monotonicity property of relative entropy. In some cases, modular energy can be related to the energy density of states and these constraints lead to…
It is well known that the spectrum condition, i.e. the positivity of the energy in every inertial coordinate system, is one of the central conceptual ingredients in model-independent approaches to relativistic quantum field theory. When one…
We solve the Schr\"odinger equation with a position-dependent mass (PDM) charged particle interacted via the superposition of the Morse and Coulomb potentials and exposed to external magnetic and Aharonov-Bohm (AB) flux fields. The…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger…
We present results on the effect of short-range, attractive interactions on the properties of balanced 2D Fermi gases in the non-superfluid (normal) phase. Our approach combines the renormalization group (RG) with perturbation theory,…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
We have examined a class of Li\'enard--Levinson--Smith (LLS) system having a stable limit cycle which demonstrates the case where the LLS theorem cannot be applied. The problem has been partly raised in a recent communication by Saha et…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
We consider ground states of a pseudo-relativistic Fermi system in the $L^2$-critical case. We prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0<a<D_{4/3,2}$, where $D_{4/3,2}\in(0, \infty)$…
In the search for QFT's that admit boundstates, we reinvestigate the two dimensional Gross-Neveu model, but with massive fermions. By computing the self-energy for the auxiliary boundstate field and the effective potential, we show that…
For a quantum confinement model, the wave function of a particle is zero outside the confined region. Due to this, the negative energy states are, in fact, square integrable. As negative energy states are not physical, we need to impose…