Related papers: Generalized Number Theoretic Spin Chain-Connection…
The pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, reaction-rate…
We derive algebraic formulas for the density matrices of finite segments of the integrable su(2) isotropic spin-1 chain in the thermodynamic limit. We give explicit results for the 2 and 3 site cases for arbitrary temperature T and zero…
We describe a modified transfer matrix renormalization group (TMRG) algorithm and apply it to calculate thermodynamic properties of the one-dimensional t-J model. At the supersymmetric point we compare with Bethe ansatz results and make…
The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition…
We propose a generalization of spin algebra using three-index objects. There is a possibility that a triple commutation relation among three-index objects implies a kind of uncertainty relation among their expectation values.
The existence of a possible connection between spin and statistics is explored within the framework of Galilean covariant field theory. To this end fields of arbitrary spin are constructed and admissible interaction terms introduced. By…
We introduce and study in detail a special class of backward continued fractions that represents a generalization of R\'enyi continued fractions. We investigate the main metrical properties of the digits occurring in these expansions and we…
We first construct a dynamical systems model which in its steady-state serves as an analytic continuation of the completed Riemann zeta function over the entire critical strip. The resulting mathematical construct involves a linear…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
A key theorem formulated in the context of functional Mellin transforms generalizes the important relationship $\exp\mathrm{tr} M=\det\exp M$. Along with the involution symmetry of the zeta function, the theorem suggests a strategy for…
We establish a novel correspondence between 4D $\mathcal N=1$ supersymmetric gauge theories on $D^2\times T^2$ and open XYZ spin chains with generalized boundary conditions, extending beyond previous 3D Bethe/gauge duality frameworks. Our…
This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several…
Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal…
Jordan-Wigner-type transformations connecting the spin-3/2 operators and two kinds of fermions are derived. A general condition of fermionizability of spins is obtained and a theorem establishing connection between half integer spins and…
We apply the recently developed thermal form factor expansion method to evaluate the real-time longitudinal spin-spin correlation functions of the spin-$\frac{1}{2}$ XXZ chain in the antiferromagnetically ordered regime at temperature…
We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads…
This paper introduces the notion of referring forms as a new metric for analyzing sequential circuits from a functional perspective. Sequential circuits are modeled as causal stream functions, the outputs of which depend solely on the past…