相关论文: On the degenerate phase boundaries

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such "phase boundaries" in which the metric is degenerate on…

Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersufaces, the conjecture that the…

This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both non-degenerate as well as degenerate states. Starting with the non-degenerate case, we show that the usual procedure of…

This paper presents a parametrization of a degenerate density matrix. The problem needs to be approached first with a diagonalized form (the spectral representation) to deal with degeneracy. Such a form is useful for this parametrization in…

The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the 2-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions…

We prove the nondegeneracy condition for stable solutions to the one-phase free boundary problem. The proof is by a De Giorgi iteration, where we need the Sobolev inequality of Michael and Simon and, consequently, an integral estimate for…

Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical…

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general…

As shown by Ashtekar in the mid 80's, general relativity can be extended to incorporate degenerate metrics. This extension is not unique, however, as one can change the form of the hamiltonian constraints and obtain an {\it alternative}…

In this paper, we characterize the geometry of solutions to one-phase inhomogeneous fully nonlinear Stefan problem with flat free boundaries under a new nondegeneracy assumption. This continues the study of regularity of flat free…

We consider a one-phase free boundary problem governed by doubly degenerate fully non-linear elliptic PDEs with non-zero right hand side, which should be understood as an analog (non-variational) of certain double phase functionals in the…

A 3d symmetry protected topological phase, by definition must have symmetry protected nontrivial boundary states, namely its 2d boundary must be either gapless or degenerate. In this work we demonstrate that once we couple a 3d SPT phase to…

We consider an one-phase free boundary problem for a degenerate fully non-linear elliptic operators with non-zero right hand side. We use the approach present in \cite{DeSilva} to prove that flat free boundaries and Lipschitz free…

We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for…

In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only…

We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…

We solve perturbative constraints and eliminate gauge freedom for Ashtekar's gravity on de Sitter background. We show that the reduced phase space consists of transverse, traceless, symmetric fluctuations of the triad and of transverse,…

In a wide class of supersymmetric theories degenerate families of the BPS-saturated domain walls exist. The internal structure of these walls can continuously vary, without changing the wall tension. This is described by hidden parameters…

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro and prove a sharp H\"older regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary…

The topological degeneracy is a characteristic of quantum phase diagram in an Ising chain with transverse field. We revisit the phase diagram at nonzero temperature of an Ising chain with two types of open boundary conditions. In this work,…