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Abstract This paper utilizes the theory of quantum diffusion to analyze the electron probability and spreading width of a wavepacket on each layer in a two-dimensional (2D) coupled system with edge disorder, aiming to clarify the effects of edge disorder on the stability of the electron periodic oscillations in 2D coupled systems. Using coupled 2D square lattices with edge disorder as an example, we show that, the electron probability and wavepacket spreading width exhibit periodic oscillations and damped oscillations, respectively, before and after the wavepacket reaches the boundary. Furthermore, these electron oscillations exhibit strong resistance against disorder perturbation with a longer decay time in the regime of large disorder, due to the combined influences of ordered and disordered site energies in the central and edge regions. Finally, we numerically verified the universality of the results through bilayer graphene, demonstrating that this anomalous quantum oscillatory behavior is independent of lattice geometry. Our findings are helpful in designing relevant quantum devices and understanding the influence of edge disorder on the stability of electron periodic oscillations in 2D coupled systems.

Strange metals exhibit universal linear-in-temperature resistivity described by a Planckian scattering rate, the origin of which remains elusive. By employing an approach inspired by quantum optics, we arrive at the coherent state representation of lattice vibrations: quantum acoustics. Utilizing this nonperturbative framework, we demonstrate that lattice vibrations could serve as active drivers in the Planckian resistivity phenomenon, challenging prevailing theories. By treating charge carriers as quantum wave packets negotiating the dynamic acoustic field, we find that a competition ensues between localization and delocalization giving rise to the previously conjectured universal quantum bound of diffusion, ħ/m*, independent of temperature or any other material parameters. This leads to the enigmatic T-linear resistivity over hundreds of degrees, except at very low temperatures. Quantum diffusion also explains why strange metals have much higher electrical resistivity than typical metals. Our work elucidates the critical role of phonons in Planckian resistivity from a unique perspective and reconsiders their significance in the transport properties of strange metals. [ABSTRACT FROM AUTHOR]

This paper utilizes the theory of quantum diffusion to analyze the electron probability and spreading width of a wavepacket on each layer in a two-dimensional (2D) coupled system with edge disorder, aiming to clarify the effects of edge disorder on the stability of the electron periodic oscillations in 2D coupled systems. Using coupled 2D square lattices with edge disorder as an example, we show that, the electron probability and wavepacket spreading width exhibit periodic oscillations and damped oscillations, respectively, before and after the wavepacket reaches the boundary. Furthermore, these electron oscillations exhibit strong resistance against disorder perturbation with a longer decay time in the regime of large disorder, due to the combined influences of ordered and disordered site energies in the central and edge regions. Finally, we numerically verified the universality of the results through bilayer graphene, demonstrating that this anomalous quantum oscillatory behavior is independent of lattice geometry. Our findings are helpful in designing relevant quantum devices and understanding the influence of edge disorder on the stability of electron periodic oscillations in 2D coupled systems. [ABSTRACT FROM AUTHOR]

In this work, the multistream quasiparticle model of collective electron excitations is applied to study the energy-density distribution of collective quantum excitations in an interacting electron gas with an arbitrary degree of degeneracy. Generalized relations for the probability current and energy density distribution are obtained which suggests a diffusive mechanism for plasmonic excitations of pure quasiparticle states at the microscopic level. The effect is applied to different cases of free quasiparticles, quasiparticles in an infinite square-well potential, and the analytic form of damping rate is obtained. The Wigner distribution and damping of excited states in phase space are also investigated. It is shown that plasmon excitations have the intrinsic tendency to decay into an equilibrium state with uniform energy density spatial distribution. It is found that plasmon levels of quasiparticles in a square-well potential are unstable decaying into an equilibrium state due to the fundamental property of collective excitations. The decay rates of pure plasmon states are determined analytically. The phase-space analysis reveals that there may be a close relation between the quantum diffusion and the Landau damping of quasiparticle states. Current research can have implications with applications in plasmonics and related fields. Current analysis can be readily generalized to include external potential, magnetic field, and electron correlation effects. [ABSTRACT FROM AUTHOR]

We study the invariant measure of the transport correlator for a chiral Hamiltonian and analyze its properties. The Jacobian of the invariant measure is a function of random phases. Then we distinguish the invariant measure before and after the phase integration. In the former case we found quantum diffusion of fermions and a uniform zero mode that is associated with particle conservation. After the phase integration the transport correlator reveals two types of evolution processes, namely classical diffusion and back-folded random walks. Which one dominates the other depends on the details of the underlying chiral Hamiltonian and may lead either to classical diffusion or to the suppression of diffusion. [ABSTRACT FROM AUTHOR]

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength of the imaginary part of the kicking. This clearly reveals the enhancement of dynamical localization by non-Hermiticity. We find, both analytically and numerically, that the quantum state are mainly populated on a very few quasieigenstates with significantly large value of the imaginary part of quasienergies. Interestingly, the average value of the inverse participation ratio of quasieigenstates decreases with the increase of the strength of the imaginary part of the kicking potential, which implies that the feature of quasieigenstates determines the stability of wavepacket's dynamics and the dynamical localization of energy diffusion. [ABSTRACT FROM AUTHOR]

H‐atom tunneling reactions play important roles in astrochemistry, but an understanding of these reactions is still in its infancy. The unique properties associated with quantum solid para‐hydrogen provide an effective environment for the generation and reactions in situ of H atoms at low temperature. Several techniques have been employed to generate H atoms to study astrochemically relevant systems that provide significant insight into the formation of complex organic molecules (COM) and help to explain the relations between the abundance of some pairs of stable species. These results introduce new concepts in astrochemistry, including H‐induced H abstraction, H‐induced fragmentation, and H‐induced uphill isomerization in darkness that have been overlooked previously. This mini‐review summarizes the state of the art in this field, discussing fundamental understanding and techniques concerning H‐atom generation, H‐tunneling reactions, and their applications; the perspectives and open questions that await further exploration are discussed. [ABSTRACT FROM AUTHOR]

Within the framework of the gas-kinetic model of a mixture of weakly interacting gas of quasiparticles—phonons and impurities—the dissipative properties of 3He–4He solid solutions are considered: diffusion, self-diffusion, and thermal conductivity in the range of concentrations and temperatures, where impurities of 3He can be considered as quasiparticles freely moving through the crystal. Explicit expressions are obtained for the dissipative coefficients of spin and mass diffusion and the coefficient of thermal conductivity. The observed in experiments on spin relaxation, heat transfer, and separation of solutions dependencies and parameters of quasiparticles are discussed. [ABSTRACT FROM AUTHOR]

We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrödinger equation in R d. We define the time-fractional derivative by the Caputo derivative. We consider the initial-value problem for the free evolution of wave packets in R d governed by the time-fractional Schrödinger equation i β ∂ t α u = − Δ u , with initial condition u (t = 0) = u 0 , parameterized by two indices α , β ∈ (0 , 1 ]. We show distinctly different long-time evolution of the mean square displacement according to the relation between α and β. In particular, asymptotically ballistic motion occurs only for α = β. [ABSTRACT FROM AUTHOR]

We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper (AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of under-damped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength. Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices. [ABSTRACT FROM AUTHOR]

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength of the imaginary part of the kicking. This clearly reveals the enhancement of dynamical localization by non-Hermiticity. We find, both analytically and numerically, that the quantum state are mainly populated on a very few quasieigenstates with significantly large value of the imaginary part of quasienergies. Interestingly, the average value of the inverse participation ratio of quasieigenstates decreases with the increase of the strength of the imaginary part of the kicking potential, which implies that the feature of quasieigenstates determines the stability of wavepacket’s dynamics and the dynamical localization of energy diffusion.

Infrared spectroscopy is used to investigate the process of molecular hydrogen ortho-to-para (o/p) conversion in solid hydrogen samples doped with small concentrations (10–50 ppm) of hydrogen atoms (H-atoms) as an impurity. The H-atoms are generated using the in situ 193 nm photolysis of N2O dopant molecules. For hydrogen crystals with relatively low initial ortho-H2 fractions (Xo ≤ 0.03), the o/p conversion kinetics at temperatures of 1.8 and 4.0 K follow kinetic equations developed previously for H-atom catalyzed o/p conversion. The measured atom catalyzed o/p conversion kinetics indicates the H-atoms are mobile under these conditions in agreement with previous ESR measurements. It has been proposed that the H-atoms diffuse by a quantum tunneling mechanism that is described as chemical diffusion. Detailed fits of the measured o/p conversion kinetic data allow the initial H-atom concentration after photolysis to be extracted assuming literature values for the H-atom recombination rate constant (H + H → H2). The measured o/p conversion kinetics show the observed o/p conversion is much less than expected based on the previously measured H-atom recombination rate constant and thus suggest that the H-atoms do not diffuse randomly through the crystal but rather diffuse preferentially in regions of high para-hydrogen content. The estimated H-atom concentrations from this study are consistent with previous ESR measurements but in conflict with kinetic studies of H-atom reactions with various dopants such as N2O. [ABSTRACT FROM AUTHOR]

Quantum dynamical semigroups represent a noncommutative analogue of (sub)Markov semigroups in classical probability: while the latter are semigroups of maps in functional spaces, the former are semigroups of maps in operator algebras having certain properties of positivity and normalization. In this paper we describe quantum dynamical semigroups, which are the noncommutative analogues of classical diffusions on R and R+, and demonstrate various properties of the semigroup and its generator depending on the boundary condition. We also give a proof of a result describing the domain of the generator of "noncommutative diffusion on R+ with extinction at 0" and give an explicit example of the trace-class operator in this domain, which does not belong to the domain of closure of the initial operator. [ABSTRACT FROM AUTHOR]

We compute the electromagnetic field created by an ultrarelativistic charged particle in vacuum at distances comparable to the particle Compton wavelength. The wave function of the particle is governed by the Klein-Gordon equation, for a scalar particle, or the Dirac equation, for a spin-half particle. The produced electromagnetic field is essentially different in magnitude and direction from the Coulomb field, induced by a classical point charge, due to the quantum diffusion effect. Thus, a realistic computation of the electromagnetic field produced in heavy-ion collisions must be based upon the full quantum treatment of the valence quarks. [ABSTRACT FROM AUTHOR]

We discuss the analysis of the experimental values of the nuclear spin-lattice and spin-spin relaxation times for the tunneling of $$^3$$ He as isotopic impurities in solid $$^4$$ He. These two relaxation times cannot be described quantitatively using a unique correlation time although it is often presented as such in the literature. In this paper, we discuss how to distinguish the high-frequency portion of the spectral densities that determine the spin-lattice relaxation rates from the low-frequency components which determine the spin-spin relaxation rates. [ABSTRACT FROM AUTHOR]

Icosahedral quasicrystals are characterised by the absence of a distinct Drude peak in their low-frequency optical conductivity and the same is true of their crystalline approximants. We have measured the optical conductivity ofi-GdCd, an icosahedral quasicrystal, and two approximants, GdCdand YCd. We find that there is a significant difference in the optical properties of these compounds. The approximants have a zero frequency peak, characteristic of a metal, whereas the quasicrystal has a striking minimum. This is the first example where the transport properties of a quasicrystal and its approximant differ in such a fundamental way. Using a generalised Drude model introduced by Mayou, we find that our data are well described by this model. It implies that the quantum diffusion of electron wave packets through the periodic and quasiperiodic lattices is responsible for these dramatic differences: in the approximants, the transport is superdiffusive, whereas the quasicrystals show subdiffusive motion of the electrons. [ABSTRACT FROM AUTHOR]

Abstract: We consider quantum diffusion of the initially localized wavepacket in one-dimensional kicked disordered system with classical coherent perturbation. The wavepacket localizes in the unperturbed kicked Anderson model. However, the wavepacket get delocalized even by coupling with monochromatic perturbation. We call the state "dynamically delocalized state". It is numerically shown that the delocalized wavepacket spread obeying diffusion law, and the perturbation strength dependence of the diffusion rate is given. The sensitivity of the delocalized state is also shown by the time-reversal experiment after random change in phase of the wavepacket. Moreover, it is found that the diffusion strongly depend on the initial phase of the perturbation. We discuss a relation between the "classicalization" of the quantum wave packet and the time-dependence of the initial phase dependence. The complex structure of the initial phase dependence is related to the entropy production in the quantum system.

The low temperature diffusivity of nanoscale crystal defects, where quantum mechanical fluctuations are known to play a crucial role, are essential to interpret observations of irradiated microstructures conducted at cryogenic temperatures. Using density functional theory calculations, quantum heat bath molecular dynamics and open quantum systems theory, we evaluate the low temperature diffusivity of self-interstitial atom clusters in tungsten valid down to temperatures of 1 K. Due to an exceptionally low defect migration barrier, our results show that interstitial defects exhibit very high diffusivity of order ${10}^{3}\,\mu {{\rm{m}}}^{2}\,{{\rm{s}}}^{-1}$ over the entire range of temperatures investigated.

We investigate the quantum dynamics in a disordered electronic lattice by the time-dependent density matrix renormalization group algorithm. The on-site energy in the lattice follows the Fibonacci sequence and the electron off-diagonally couples to a sub-Ohmic phonon bath. It is found that the slope of the inverse participation ratio versus the coupling strength undergoes a sudden change that indicates a transition from static to dynamic localization, and that the generated polarons coherently diffuse via hopping-like processes, evidenced by the saturated entanglement entropy, providing a novel scenario for a transportation mechanism in strongly disordered systems. Moreover, the mean-square displacement is revealed to be insensitive to the coupling strength, implying the quantum diffusion behavior survives the energy disorder that prevails in real organic materials.

The 180 $$^{\circ }$$ twin boundary (stacking fault) is investigated in the hexagonal close-packed (hcp) lattice. It is shown that the interatomic interaction between neighbors within the boundary lowers symmetry as compared with that in hcp phase. An initial spherical form (hcp phase) is elongated along the shift direction of the atomic planes inside the boundary. We find the wave functions of the helium atom for (i) the spherical oscillator (within the hcp phase) and (ii) an anisotropic one (inside the boundary). To estimate the parameters of the thermodynamic potential we apply the model of spheres and ellipsoids for the isosurfaces of the probability. Method of the successive approximations is applied for the self-consistent description of the distorted wave functions of atoms. It is shown that the quantum behavior of the boundary atoms causes the following effects: (i) increasing of degree of overlap of the atomic wave functions within the twin boundaries, (ii) increasing of the quantum diffusion inside the twin boundaries, (iii) decreasing of energy and broadening of the boundary in comparison with the classical case. [ABSTRACT FROM AUTHOR]

Recently, the occurrence of log-periodic oscillations in the quantum dynamics of electrons was reported for the one-dimensional Fibonacci quasicrystal by Lifshitz and Even-Dar Mandel. We apply a real-space renormalization group approach to show that these log-periodic oscillations are related to the underlying quasiperiodic structure of the Fibonacci quasicrystal. We find that they originate from the superposition of bonding and antibonding states associated to strongly coupled atoms in the chains, and that they show a hierarchical structure closely related to the atomic configurations. [ABSTRACT FROM PUBLISHER]

We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact, analytical solution of the model yields the transient behavior of the coupled fermion systems evolving to a final steady state, whereas the long-time behavior is determined by a power law rather than by exponential decay. Similar results are obtained for the entropy production which is proportional to the diffusion current. [ABSTRACT FROM AUTHOR]