arXiv subjects

Anvar Khujakulov

Publications and source records attributed to Anvar Khujakulov.

4 recordsLinked to original sources

arXiv2026

Real-time probing of quadrupolar contributions to the absorption cross section of non-periodic systems

The non-perturbative evaluation of multipolar cross sections is essential for probing atomic and molecular responses to spatially inhomogeneous electric fields characteristic of nanoscale environments where the conventional dipole approximation breaks down. Taking the hydrogen atom as an analytical and numerical benchmark, we map in real time quadrupole interactions driven by instantaneous electric field gradients. Our study explores two distinct interaction regimes. Under a uniform field, quadrupolar responses are activated by multi-step dipole transitions, responsible for sub-1~eV excited-state absorption. Conversely, under pure spatial gradients, the weak-field response is dominated by the single-photon $1s \to 3d$ quadrupole resonance at 12.1~eV, while strong gradients induce low-energy stimulated emission via transiently driven coherent populations. This dynamical analysis is complemented by a rigorous evaluation of the symmetry aspects of the quadrupole response and the applied electric field. This methodology establishes the theoretical and computational foundation for future non-perturbative multipole simulations of molecules and nanostructures in the near-field regime.

cond-mat.quant-gas↗

arXiv2026

Relativistic Effects on Photoabsorption Cross Sections of Highly Charged Ions

The study of highly charged ions offers a unique platform for probing the breakdown of non-relativistic theory under the influence of extreme electromagnetic environments. Here, we investigate the photoabsorption of highly charged ions within the dipole approximation using both the time-dependent Schrödinger equation (TDSE) and the time-dependent Dirac equation (TDDE), modelling the external field as an instantaneous broadband excitation. Nonrelativistic scaling relations with respect to the nuclear charge are utilized as a diagnostic tool to systematically identify and quantify relativistic contributions. Within the purely nonrelativistic TDSE framework, these scaling relations hold exactly, allowing the absorption spectra of arbitrary highly charged ions to be inferred directly from a neutral hydrogenic reference. However, as the nuclear charge increases, relativistic effects become dominant through a sizeable blue shift in the absorption cross section, due to the relativistic enhancement of the binding energy. We further evaluate semi-relativistic TDSE approximations by direct comparison with full TDDE simulations, assessing their predictive power and establishing the regimes where a full Dirac treatment is indispensable for quantitative accuracy.

cond-mat.other↗

arXiv2017

Fast forward of adiabatic control of tunneling states

By developing the preceding work on the fast forward of transient phenomena of quantum tunneling by Khujakulov and Nakamura (Phys. Rev. {\bf A 93}, 022101 (2016) ), we propose a scheme of the exact fast forward of adiabatic control of stationary tunneling states with use of the electromagnetic field. The idea allows the acceleration of both the amplitude and phase of wave functions throughout the fast-forward time range. The scheme realizes the fast-forward observation of the transport coefficients under the adiabatically-changing barrier with the fixed energy of an incoming particle. As typical examples we choose systems with (1) Eckart's potential with tunable asymmetry and (2) double $δ$-function barriers under tunable relative height. We elucidate the driving electric field to guarantee the stationary tunneling state during a rapid change of the barrier and evaluate both the electric-field-induced temporary deviation of transport coefficients from their stationary values and the modulation of the phase of complex scattering coefficients

quant-ph↗

arXiv2016

Scheme for accelerating quantum tunneling dynamics

We propose a scheme of the exact fast-forwarding of standard quantum dynamics for a charged particle. The present idea allows the acceleration of both the amplitude and phase of the wave function throughout the fast-forward time range and is distinct from that of Masuda-Nakamura (e.g., Proc. R. Soc. A {\bf 466}, 1135 (2010)) which enabled acceleration of only the amplitude of the wave function on the way. We shall apply the proposed method to the quantum tunneling phenomena and obtain the electro-magnetic field to ensure the rapid penetration of wave functions through a tunneling barrier. Typical examples described here are: 1) an exponential wave packet passing through the delta-function barrier; 2) the opened Moshinsky shutter with a delta-function barrier just behind the shutter. We elucidate the tunneling current in the vicinity of the barrier and find the remarkable enhancement of the tunneling rate (: tunneling power) due to the fast-forwarding. In the case of a very high barrier, in particular, we present the asymptotic analysis and exhibit a suitable driving force to recover a recognizable tunneling current. The analysis is also carried out on the exact acceleration of macroscopic quantum tunneling with use of the nonlinear Schrödinger equation which accommodates a tunneling barrier.

quant-ph↗