Related papers: Symmetric Potentials Beget Symmetric Ground States
Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of…
A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists,…
Symmetric teleparallel gravity is shown to be integrable in the presence of boundaries, given the consistent implementation of constraints in the covariant phase space formalism.
We consider the static potential in theories exhibiting spontaneous symmetry breaking. We use our findings to calculate the static potential of the Standard Model at one-loop order. We do so in both the Wilson loop and scattering amplitude…
In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p-Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the…
We present two methods to prove the uniqueness of normalized ground states. We will first discuss the key ideas and ingredients of each method. Then, we will apply them to various classes of PDEs. Our approach is applicable to other…
A classical lattice gas model with translation-invariant finite range competing interactions, for which there does not exist an equivalent translation-invariant finite range nonfrustrated potential, is constructed. The construction uses the…
We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature.…
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
We study the entanglement feature of the ground state of a system composed of spin 1 and 1/2 parts. The concurrence vector is shown to be consistent with the measurement of von Neumann entropy for such system. In the light of the ground…
The ${\cal PT}$ symmetric version of the generalised Ginocchio potential, a member of the general exactly solvable Natanzon potential class is analysed and its properties are compared with those of ${\cal PT}$ symmetric potentials from the…
We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent states, very well captures the fundamental…
The global correlation in the observed variation with mass number of the $E2$ and summed $M1$ transition strengths is examined for rare earth nuclei. It is shown that a theory of correlated $S$ and $D$ fermion pairs with a simple pairing…
Based on an iterative method for solving the goundstate of Schroedinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the…
The space-like asymptotic limit of the bilocal composite field of the state consisting of a nucleus and an electron is studied. It is shown that the resulting local field of an atom satisfies the proper commutation relations in the…
We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new…
We introduce and analyze a task that we call symmetrization, in which a state of a quantum system, associated with a symmetry group, is transformed by a random unitary operation to a symmetric state. Each element of the unitary ensemble is…
We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential…
We formalize and generalize the concept of a topological state-sum construction using the language of tensor networks. We give examples for constructions that are possibly more general than all state-sum constructions in the literature that…
We find necessary and sufficient conditions for $P$-equivalence of arbitrary matrices and $P$-congruence of symmetric and alternating matrices, where $P$ is standard parabolic subgroup of $GL_n(F)$ and $F$ is an arbitrary field.