We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.

In this paper, we attempt to reconstruct one of the last and incomplete projects of Volodya Geyler. We study the motion of a quantum particle in the plane to which a halfline lead is attached, assuming that the particle has spin and the plane component of the Hamiltonian contains a spin-orbit interaction, of Rashba or Dresselhaus type. We construct a class of admissible Hamiltonians and derive an explicit expression for the Green function, which is applied to scattering in a system of this kind.

The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that: 1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; 2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; 3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that, with respect to the steady state, general Markov processes admit a unified and self-consistent non-equilibrium thermodynamic formulation, regardless of underlying detailed models.

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We study two-dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. For a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. Applying our results to the four-point function of the Z_2 twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for h ≥ c/12.

Let $K_k$, $C_k$, $T_k$, and $P_{k}$ denote a complete graph on $k$ vertices, a cycle on $k$ vertices, a tree on $k+1$ vertices, and a path on $k+1$ vertices, respectively. Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this paper, we determine the values of $\sigma (K_{r+1}-H, n)$ for $n\geq 4r+10, r\geq 3, r+1 \geq k \geq 4$ where $H$ is a graph on $k$ vertices which contains a tree on $4$ vertices but not contains a cycle on $3$ vertices. We also determine the values of $\sigma (K_{r+1}-P_2, n)$ for $n\geq 4r+8, r\geq 3$.

In addition to the conventional renormalized-coupling-constant picture, point interactions in two and three dimensions are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.

We discuss spectral and resonance properties of a Hamiltonian describing motion of an electron moving on a hybrid surface consisting on a halfline attached by its endpoint to a plane under influence of a constant magnetic field which interacts with its spin through a Rashba-type term.

We propose a model for scattering in a flat resonator with a thin antenna. The results are applied to rectangular microwave cavities. We compute the resonance spacing distribution and show that it agrees well with experimental data provided the antenna radius is much smaller than wavelengths of the resonance wavefunctions.

Point interactions described by formal shaped potentials were used in quantum mechanics from the early thirties. It lasted several decades, however, until a proper way to handle the corresponding Schrdinger operators was found. Following the observation of Berezin and Faddeev [4], the problem was studied systematically in the eighties. The results are summarized in the monograph [1], references to some recent work are given, eg, in [2, 8]. In its present form the pointinteraction method represents a versatile tool for constructing solvable models whose power has not been yet, to our opinion, appreciated fully in the physical community. Within the standard quantum mechanical formalism point interactions can be constructed as long as the configuration space dimension does not exceed three, and they can be interpreted as limits of suitable families of squeezed potentials. In the onedimensional case the limiting argument admits a straightforward interpretation, because the pointinteraction coupling constant is just the integral of the approximating potential: a slow particle on the line with a wellspread wavefunction sees only the average value of a localized potential. In distinction to that the approximation by scaled potentials in dimension two and three requires existence of a zeroenergy resonance and a particular couplingconstant renormalization; a detailed discussion of the related mathematical problems can be found in [1, 9]. This gives these point interactions a flavour of something exceptional, for instance, one is led to believe that they cannot be used to model welllocalized repulsive potentials. That would have consequences