Related papers: Running Boundary Condition
We discuss the quantum mechanics of a particle restricted to the half-line $x > 0$ with potential energy $V = \alpha/x^2$ for $-1/4 < \alpha < 0$. It is known that two scale-invariant theories may be defined. By regularizing the near-origin…
Boundary critical phenomena are studied in the 3- State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and…
Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be…
In manifolds with spatial boundary, BRST formalism can be used to quantize gauge theories. We show that, in a $U(1)$ gauge theory, only a subset of all the boundary conditions allowed by the self-adjointness of the Hamiltonian preserves…
Starting with a quantum particle on a closed manifold without boundary, we consider the process of generating boundaries by modding out by a group action with fixed points, and we study the emergent quantum dynamics on the quotient…
The possibility of treating boundary conditions in terms of a bilocal dynamical field is formalized in terms of a boundary action. This allows for a simple path-integral perturbation theory approach to physical effects such as radiation…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
We study the possibility of supersymmetry (SUSY) in quantum mechanics in one dimension under the presence of a point singularity. The system considered is the free particle on a line R or on the interval [-l, l] where the point singularity…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…
We develop a formalism to describe the formation of bound states in quantum field theory using an exact renormalization group flow equation. As a concrete example we investigate a nonrelativistic field theory with instantaneous interaction…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group flow on the space of boundary conditions is generated by the boundary beta…
The boundary beta-function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula…
Boundary effect is a widespread idea in many-body theories. However, it is more of a conceptual notion than a rigorously defined physical quantity. One can quantify the boundary effect by comparing two ground states of the same physical…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of…
We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles…
We investigate nonrelativistic quantum mechanics on the discretized half-line, constructing a one-parameter family of Hamiltonians that are analogous to the Robin family of boundary conditions in continuum half-line quantum mechanics. For…
Using the properties of defect lines, we study boundary renormalisation group flows. We find that when there exists a flow between maximally symmetric boundary conditions "a" and "b" then there also exists a boundary flow between "c x a"…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…