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We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT)…
The behaviour of the quark coefficient function for the longitudinal structure function F_L in deep-inelastic scattering is investigated for large values of the Bjorken variable x. We combine a highly plausible conjecture on the large-x…
The behavior of spin-1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
We review how a specific resummation of the so-called "delta-expansion", applied to the QCD Lagrangian, transforms the ordinary perturbative expansion in $\alpha_s$ into an expansion in an arbitrary mass parameter, around the basic scale…
We analytically derive a decomposition of the lattice fermion determinant for Wilson's Dirac operator with chemical potential into winding sectors, i.e., factors with a fixed number of quarks. Dividing the lattice into four domains, the…
Defining a scale of $k$-modes of the quantum fluctuations during inflation through the dynamical horizon crossing condition $k = aH$ we go from the physical $t$ variable to $k$ variable and solve the equations of cosmological first-order…
In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation, write the first and second-order equations from it, and then we solve…
We present a theoretical analysis of phase separation in the presence of a spatially periodic forcing of wavenumber q traveling with a velocity v. By an analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model we find…
The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the momentum and $a^2$. Starting from this chiral…
We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power…
We investigate the quantum-classical transition in the delta-kicked rotor and the attainment of the classical limit in terms of measurement-induced state-localization. It is possible to study the transition by fixing the environmentally…
The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated by linearly polarized light is addressed through the solution of the time-dependent Schr\"odinger equation for the two-dimensional Dirac Hamiltonian via the Floquet…
We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially…
We develop the regularity theory for solutions to space-time nonlocal equations driven by fractional powers of the heat operator $$(\partial_t-\Delta)^su(t,x)=f(t,x),\quad\hbox{for}~0<s<1.$$ This nonlocal equation of order $s$ in time and…
In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a…
I consider the problem of self-oscillatory systems undergoing a homogeneous Hopf bifurcation when they are submitted to an external forcing that is periodic in time, at a frequency close to the system's natural frequency (1:1 resonance),…