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Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
Quantum escapes of a particle from an end of a one-dimensional finite region to $N$ number of semi-infinite leads are discussed by a scattering theoretical approach. Depending on a potential barrier amplitude at the junction, the…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…
The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decays. In the limit of very high…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
We calculate the dynamical relativistic corrections, originating from radiative one-gluon-exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of Light-Front Dynamics. Comparison with the…
We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the…
We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the $\mathrm{T}\overline{\mathrm{T}}$ deformation and the recently introduced hard rod deformation. We…
We explore the two-dimensional motion of relativistic electrons when they are trapped in magnetic fields having spatial power-law variation. Its impacts include lifting of degeneracy that emerged in the case of the constant magnetic field,…
We develop a field theory with dissipation based on a finite range of wave propagation and associated gapped momentum states in the wave spectrum. We analyze the properties of the Lagrangian and the Hamiltonian with two scalar fields in…
We revisit Sakurai's remark on the regularities of lepton-pair widths for mesons, extending the panorama to radiative $X \to \gamma \gamma$ and total decays. The regularities persist, and somehow surprisingly some of them seem to relate…
The dissipative quantum electromagnetics is introduced in a comprehensive manner as a field-matter-bath coupling problem. First, the matter is described by a cluster of Lorentz oscillators. Then the Maxwellian free field is coupled to the…
We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. Two separate contributions to the quantum…
We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In…
Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…