We show that classical DNA unzipping transition, which is equivalently described by quantum mechanical localization-delocalization transition in the ground state of non-Hermitian single impurity Hatano-Nelson Hamiltonian, underpinned generalized parity (P)-time reversal (T) symmetry breaking transition. also study one-dimensional discretized version model presence and random disorder on a finite-size lattice. These discrete models are useful to adsorbed polymer from surface. Our results...

We consider infinitesimal field-dependent BRS transformations. show that they can be integrated to yield finite transformations and have the same form. discuss a number of applications latter. for certain special parameters (evaluated in closed form), these used connect Faddeev-Popov effective action linear gauge with parameter \ensuremath{\lambda} (i) most general BRS--anti-BRS symmetric gauges, (ii) quadratic (iii) another distinct \ensuremath{\lambda}'. In each case, extra terms latter...

In this paper, we present an analysis of the equation $\ddot{x} - (1/2x) \dot{x}^2 + 2 \omega^2 x 1/8x = 0$, where $\omega > 0$ and $x x(t)$ is a real-valued variable. We first discuss appearance from position-dependent-mass scenario in which mass profile goes inversely with $x$, admitting singularity at 0$. The associated potential also singular splitting real axis into two halves, i.e., < dynamics exactly solvable for both branches so definiteness, stick to branch. Performing canonical...

The polymer POPTN was investigated to elucidate its magnetic and optoelectronic properties, with particular emphasis on charge carrier mobility, dichroic behaviour, interactions. Electron paramagnetic resonance (EPR) studies confirmed delocalization over the naphthalene side chains, contributing observed behaviour at room temperature. Temperature-dependent revealed higher temperatures transitioning weak ferromagnetism below 10 K. Curie-Weiss analysis indicated antiferromagnetic (AFM)...

In this paper, we introduce and analyze the Smith-Volterra-Cantor potential of power n, denoted as SVCρ,n. Bridging gap between general Cantor GC SVC systems, novel offers a fresh perspective on Cantor-like systems within quantum mechanics that unify fractal non-fractal potentials. Utilizing Super Periodic Potential formalism, derive close form expression transmission probability TG(k). Notably, system exhibits exceptionally sharp resonances, characteristic distinguishes it from other...

Abstract To bridge the fractal and non-fractal potentials we introduce concept of generalized unified Cantor potential (GUCP) with key parameter $N$ which represents count at stage $S=1$. This system is characterized by total span $L$, stages $S$, scaling $\rho$ two real numbers $\mu$ $\nu$. Notably, polyadic (PCP) minimal lacunarity a specific instance within GUCP paradigm. Employing super periodic (SPP) formalism, formulated closed-form expression for transmission probability $T_{S}(k, N)$...

Abstract To bridge the fractal and non-fractal potentials we introduce concept of generalized unified Cantor potential (GUCP) with key parameter N which represents count at stage S = 1. This system is characterized by total span L , stages scaling ρ two real numbers µ ν . Notably, polyadic minimal lacunarity a specific instance within GUCP paradigm. Employing super periodic formalism, formulated closed-form expression for transmission probability <mml:math...

We develop the off-shell nilpotent finite field dependent BRST transformations and show that for different choices of parameter these connect generating functionals corresponding to effective theories. also construct both on-shell anti-BRST tranformations Yang Mills theories play similar role in connecting Analogous transformations, non-trivial Jacobians path integral measure which arise due are responsible new results. consider several explicit examples each case demonstrate

We consider the Gribov-Zwanziger (GZ) theory with appropriate horizon term which exhibits nilpotent BRST invariance. This infinitesimal transformation has been generalized by allowing parameter to be finite and field dependent (FFBRST). By constructing field-dependent we show that generating functional of GZ is related Yang-Mills (YM) through FFBRST transformation.

We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories in context generalized BRST transformations with a finite field-dependent parameter. In usual Faddeev-Popov (FP) such (FFBRST) do not leave generating functionals invariant as path integral measure changes non-trivial way for transformations. Here we show that FFBRST transformation, appropriate choice parameter, is symmetry formalism. The parameter chosen contribution from Jacobian adjusted fixed fermions...

We generalize the BRST transformations in Abelian rank-2 tensor field theory by allowing parameter to be finite and field-dependent show that such play crucial role studying 2-form gauge noncovariant gauges. The generating functionals different effective theories are connected through these generalized with choice of parameter. further consider generalization anti-BRST even dependent relate functional for theories. Such BRST/anti-BRST useful connecting corresponding Field/antifield...