Related papers: A Simple Method for Computing Soliton Statistics
Simulations of supersymmetric models on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low…
We propose to replace the classical Lorentz group with a compact semisimple Lie group. The results are rendered via the formalism of superspinors - objects identifiable as particles or antiparticles, and governed by the Fermi-Dirac…
We present the saddle-point approximation for the effective Hamiltonian of the quantum kink in two-dimensional linear sigma models to all orders in the time-derivative expansion. We show how the effective Hamiltonian can be used to obtain…
Using the Wronskian representation of $\tau$-function, one can investigate the resonant structure of kink-soliton and line-soliton of the modified KP equation. It is found that the resonant structure of the the soliton graph is obtained by…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. Its mean and variance are known, but results for its median and mode are difficult to obtain, although a few cases have been solved and upper/lower…
A re-formulated, non-Hermitian version of the Witten's supersymmetric quantum mechanics is presented. Its use of pseudo-Hermitian (so called PT symmetric) Hamiltonians is reviewed and illustrated via several forms of an innovated…
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localised packet and which preserves this localisation in time. A soliton is a solitary wave which exhibits some strong form of stability so that…
We show that there are solitons with fractional fermion number in integrable $N$=2 supersymmetric models. We obtain the soliton S-matrix for the minimal, $N$=2 supersymmetric theory perturbed in the least relevant chiral primary field, the…
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…
A quantum integrability index was proposed in \cite{KMS}. It systematizes the Goldschmidt and Witten's operator counting argument \cite{GW} by using the conformal symmetry. In this work we compute the quantum integrability indexes for the…
We give a simple toy model to study a famous Jahn-Teller type molecule. Finite lifetime due to non-adiabatic coupling and finite temperature effect results in the effective Hamiltonian to be non-Hermitian. This effect pulls a conical…
A previous approach with Fermi-Dirac distributions for fermion partons is here improved to comply with the expected low $x$ behaviour of structure functions. We are so able to get a fair description of the unpolarized and polarized…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different…
We consider non-topological, "bell-shaped" localized and regular solutions available in some 1+1 dimensional scalar field theories. Several properties of such solutions are studied, namely their stability and the occurence of fermion bound…
The conjecture that the elementary fermions are knotted flux tubes permit the construction of a phenomenology that is not accessible from the standard electroweak theory. In order to carry these ideas further we have attempted to formulate…
We give a definition for the notion of statistics in the lattice-theoretical (or propositional) formulation of quantum mechanics of Birchoff, von Neumann and Piron. We show that this formalism is compatible only with two types of…
A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian.…
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…
The Korteweg-de Vries and Benjamin-Ono nonlinear wave equations can describe solitary waves, all of which propagate in the same direction and which emerge from collisions with their shapes unchanged. There are technical challenges to giving…