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The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated…
Study of far-from-equilibrium thermalization dynamics in quantum materials, including the dynamics of different types of quasiparticles, is becoming increasingly crucial. However, the inherent complexity of either the full quantum…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
Using a hybrid approach, based on the recursion relations for shape invariant potentials developed by Das and Huang and a time-dependent tranformation of variables, we derive the propagator for a radial oscillator. Although this is not a…
We present an investigation of various gauge invariant definitions of the $q\bar q$ Bethe-Salpeter (BS) amplitude for mesons in lattice QCD, and compare them to the Coulomb and Landau gauge BS amplitudes. We show that the gauge invariant BS…
We investigate the light quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze…
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is…
We summarize developments concerning the quark mass dependence of nucleon magnetic moments and the axial-vector coupling constant g_A. The aim is to explore the feasibility of chiral effective field theory methods for the extrapolation of…
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
Restrictions imposed on the (electromagnetic or weak) current operator by its commutation relations with the representation operators of the Poincare group are considered in detail. We argue that the present theory of deep inelastic…
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…
A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic…
Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the…
A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to…
The Coulomb-hadron interference effects are examined at small and large $t$. The methods for the definition of spin-dependent parts of hadron scattering amplitude are presented. The additional contributions to analyzing power $A_N$ and the…
It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion…
By minimizing the difference between the left- and the right-hand sides of the many-body time-dependent Schr\"{o}dinger equation with the Slater-determinant wave-function, we derive a non-adiabatic and self-interaction free time-dependent…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…
We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet…