arXiv subjects

Vladimir U. Nazarov

Publications and source records attributed to Vladimir U. Nazarov.

15 recordsLinked to original sources

arXiv2026

In defence of the Ehrenfest mean-field molecular dynamics

Re-visiting the problem of the coupled electronic--nuclear motion, we prove that the so called `mean-field' Ehrenfest picture is an exact theory, rather than an approximation, in the classical limit for nuclei. By establishing its full equivalence to the much more involved Exact Factorization approach to the problem (Abedi {\it et al.}, Europhys. Lett. {\bf 106}, 33001 (2014)), our conclusion rehabilitates the mean-field Ehrenfest molecular dynamics as a simple, effective, while formally exact scheme, amenable to the use within the framework of the time-dependent density functional theory.

quant-ph↗

arXiv2026

Many-body interactions in the dielectric theory of stopping power of solids for classical and quantum projectiles

We take account of the many-body dynamic interactions by including the wave-vector and frequency-dependent exchange and correlations (xc) kernel $f_{xc}(\qv,ω)$ in the framework of the dielectric theory of the stopping power of crystals for moving charges. The cases of classical and quantum projectiles are considered. We find that (I) the role of the xc effects in slowing of charges in crystalline solids is more pronounced than it is within the jellium model and (II) For velocities below the stopping maximum, inclusion of xc leads to the improvement of the comparison of the theory with experiment over a range of solid targets. On the other hand, in the high-velocity regime, the role of the dynamic xc proves negligible, which does not contradict experiment, and which we substantiate analytically within the jellium model of the target. The input to our theory is the microscopic dielectric matrix $ε_{\Gv \Gv'}(\qv,ω)$ within the random phase approximation (i.e., with neglect of $f_{xc}$), the calculation of which matrix is implemented in the existing solid-state codes.

cond-mat.mtrl-sci↗

arXiv2025

Exact-factorization framework for electron-nuclear dynamics in electromagnetic fields

The Exact Factorization (EF) theory aims at the separation of the nuclear and electronic degrees of freedom in the many-body (MB) quantum mechanical problem. Being formally equivalent to the solution of the MB Schrödinger equation, EF sets up a strategy for the construction of efficient approximations in the theory of the correlated electronic-nuclear motion. Here we extend the EF formalism to incorporate the case of a system under the action of an electromagnetic field. An important interplay between the physical magnetic and the Berry-curvature fields is revealed and discussed within the fully non-adiabatic theory. In particular, it is a known property of the Born-Oppenheimer approximation that, for a neutral atom in a uniform magnetic field, the latter is compensated by the Berry-curvature field in the nuclear equation of motion (\citet{Yin-92}). From an intuitive argument that the atom must not be deflected by the Lorentz force from a straight line trajectory, it has been conjectured that the same compensation should occur within the EF theory as well. We give a rigorous proof of this property.

quant-ph↗

arXiv2025

Stopping power of electron liquid for slow quantum projectiles

We revisit the problem of deceleration of a charge moving in a medium. Going beyond the traditional approach, which relies on Ehrenfest dynamics, we treat the projectile fully quantum mechanically, on the same footing as the electrons of the target. In order to separate the dynamics of the projectile from that of the electrons, we employ the Exact Factorization method. We illustrate the resulting theory by applying it to the problem of the stopping power (SP) of a jellium-model metal for slowly moving charges. The quantum mechanical nature of particles manifests itself remarkably in the differences in the SP for projectiles of the same charge moving with the same velocity, but having different masses.

cond-mat.mtrl-sci↗

arXiv2025

Viscous AC current-driven nanomotors

The recent discovery that electrons in nano-scale conductors can act like a highly viscous liquid has triggered a surge of research activities investigating consequences of this surprising fact. Here we demonstrate that the electronic viscosity has an enormous influence on the operation of a prototypical AC-current-driven nano-motor. The design of this prototype consists of a diatomic molecule immersed in an otherwise homogeneous electron liquid which carries an AC current. The motion of the diatomic is determined by a subtle balance between the current-induced forces and electronic friction. By ab-initio time-dependent density-functional simulations we demonstrate that the diatomic performs a continuous rotation provided the amplitude and frequency of the imposed AC current lie within certain islands of stability. Outside these islands the nuclear motion is either chaotic or comes to a stand-still. The proposed design of the nano-motor is the conceptually simplest realization of the idea of an molecular waterwheel sandwiched between conducting leads

cond-mat.mes-hall↗

arXiv2024

Exchange kernel $f^h_x(q,ω)$ of electron liquid from the variational principle of McLachlan

By minimizing, in the $L_2$ norm, the difference between the left- and the right-hand sides of the time-dependent Schrödinger equation, the variational principle of McLachlan (McLVP) [A. McLachlan, Molecular Physics {\bf 8}, 39 (1964)] provides a powerful tool for the generation of equations of motion. If the trial wave function is the Slater determinant, McLVP produces a temporally and spatially nonlocal exchange potential [V. U. Nazarov, Phys. Rev. B {\bf 87}, 165125 (2013)]. We study the performance of the corresponding wave-vector and frequency-dependent exchange kernel $f^h_x(q,ω)$ of the homogeneous electron liquid. While the McLVP-based $f^h_x(q,ω)$ lacks correlations by construction, we find that it accurately accounts for exchange, reproducing features in the quantum Monte Carlo data, which the known constraint-based kernels miss. We argue that the complementary use of the McLVP- and the constraint-based exchange-correlation kernels will enhance the performance of the linear response time-dependent density functional theory of the electron liquid.

cond-mat.str-el↗

arXiv2024

Viscous current-induced forces

We study the motion (translational, vibrational, and rotational) of a diatomic impurity immersed in an electron liquid and exposed to electronic current. An approach based on the linear response time-dependent density functional theory combined with the Ehrenfest dynamics leads to a system of linear algebraic equations, which account for the competing and counteracting effects of the current-induced force (electron wind) and the electronic friction. These forces, by means of the dynamic exchange-correlation kernel $f_{xc}({\bf r},{\bf r}',ω)$, include the electronic viscosity contribution. Starting from the ground state at the equilibrium inter-nuclear distance and applying a current pulse, we observe three phases of the motion: (I) acceleration due to the prevalence of the current-induced force, (II) stabilization upon balancing of the two forces, and (III) deceleration due to the friction after the end of the pulse. The viscous contribution to the force largely increases the acceleration (deceleration) at the first (third) phase of the process. For the aluminium HEG electron density, we find this correction to amount to up to 70% of the total electron wind and friction effects.

cond-mat.mtrl-sci↗

arXiv2022

High frequency limit of spectroscopy

We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency $ω_0$ and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schrödinger equation in the high-$ω_0$ limit, we find that, to the leading order in $ω_0^{-1}$, a perfect self-cancellation of the system's linear response occurs as the pulse switches off. Surprisingly, the system's observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology.

cond-mat.mes-hall↗

arXiv2021

Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems

The IP-theorem of the Kohn-Sham (KS) density functional theory (DFT) states that the energy of the highest occupied molecular orbital (HOMO) $ε_{HOMO}$ equals the negative of the first ionization potential (IP), thus ascribing a physical meaning to one of the eigenvalues of the KS hamiltonian. We scrutinize the fact that the validity of the IP-theorem relies critically on the electron density $n({\bf r})$, far from the system, to be determined by HOMO only, behaving as $n({\bf r}) \underset{r\to\infty}{\sim} e^{- 2 \sqrt{-2 ε_{HOMO}} r}$. While this behavior always holds for finite systems, it does not hold for mesoscopic ones, such as quasi-two-dimensional (Q2D) electron gas or Q2D crystals. We show that this leads to the violation of the IP-theorem for the latter class of systems. This finding has a strong bearing on the role of the KS valence band with respect to the work-function problem in the mesoscopic case. Based on our results, we introduce a concept of the IP band structure as an observable alternative to its unphysical KS counterpart. A practical method of the determination of IP band structure in terms of DFT quantities is provided.

cond-mat.mes-hall↗

arXiv2019

Many-body quantum dynamics by the reduced density matrix based on the time-dependent density functional theory

We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant $λ$ naturally arises. We then find the reduced density matrix $ρ_λ({\bf r},{\bf r}',t)$, which, by construction, has the $λ$-independent diagonal elements $ρ_λ({\bf r},{\bf r},t)=n({\bf r},t)$, $n({\bf r},t)$ being the particle density. The off-diagonal elements of $ρ_λ({\bf r},{\bf r}',t)$ contribute importantly to the processes, which cannot be treated via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in $λ$, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.

cond-mat.mes-hall↗

arXiv2018

Cross-over between collective and independent-particle excitations in quasi-2D electron gas with one filled miniband

While it has been recently demonstrated that, for quasi-2D electron gas (Q2DEG) with one filled miniband, the dynamic exchange $f_x$ and Hartree $f_H$ kernels cancel each other in the low-density regime $r_s\rightarrow \infty$ (by half and completely, for the spin-neutral and fully spin-polarized cases, respectively), here we analytically show that the same happens at arbitrary densities at short distances. This motivates us to study the confinement dependence of the excitations in Q2DEG. Our calculations unambiguously confirm that, at strong confinements, the time-dependent exact exchange excitation energies approach the single-particle Kohn-Sham ones for the spin-polarized case, while the same, but less pronounced, tendency is observed for spin-neutral Q2DEG.

cond-mat.mes-hall↗

arXiv2017

Electron energy-loss spectroscopy of quasi-two-dimensional crystals: Beyond the energy-loss functions formalism

A consistent theory of electron energy-loss spectroscopy (EELS) includes two indispensable elements: (i) electronic response of the target system and (ii) quantum kinematics of probing electrons. While for the bulk materials and their surfaces separating these two aspects and focusing on the former is the usual satisfactory practice (the energy-loss functions formalism), we show that, for quasi-2D crystals, the interplay of the system's electronic response and the details of the probe's motion affects EEL spectra dramatically, and it must be taken into account for the reliable interpretation of the experiment. To this end, we come up with a unified theory which, on the same footing, treats both the long- and short-range scattering, within both the transmission and reflection experimental setups. Our calculations performed for graphene reveal a phenomenon of a strong coupling between the $π+σ$ plasmon excitation and elastic {\it scattering resonances}. Freed from the conventions of the energy-loss functions formalism, our theory serves as a consistent and systematic means of the understanding of the EELS of quasi-2D materials.

cond-mat.mes-hall↗

arXiv2017

Quasi-low-dimensional electron gas with one populated band as a testing ground for time-dependent density-functional theory

We find the analytical solution to the time-dependent density-functional theory (TDDFT) problem for the quasi-low-dimensional (2D and 1D) electron gas (QLDEG) with only one band filled in the direction perpendicular to the system extent. The theory is developed at the level of TD exact exchange and yields the exchange potential as an explicit nonlocal operator of the spin-density. The dressed interband (image states) excitation spectra of the Q2DEG are calculated, while the comparison with the Kohn-Sham (KS) transitions provides the insight into the qualitative and quantitative role of the many-body interactions. Important cancellations between the Hartree $f_H$ and the exchange $f_x$ kernels are found in the low-density limit, shedding light on the interrelations between the KS and many-body excitations.

cond-mat.mes-hall↗

arXiv2015

Negative static permittivity and violation of Kramers-Kronig relations in quasi-two-dimensional crystals

We investigate the wave-vector and frequency-dependent screening of the electric field in atomically thin (quasi-two-dimensional) crystals. For graphene and hexagonal boron nitride we find that, above a critical wave-vector $q_c$, the static permittivity $\varepsilon(q \! > \!q_c,ω\! = \!0)$ becomes negative and the Kramers-Kronig relations do not hold for $\varepsilon(q \! > \! q_c,ω)$. Thus, in quasi-two-dimensional crystals, we reveal the physical confirmation of a proposition put forward decades ago (Kirzhnits, 1976), allowing for the breakdown of Kramers-Kronig relations and for the negative static permittivity. In the vicinity of the critical wave-vector, we find a giant growth of the permittivity. Our results, obtained in the {\it ab initio} calculations using both the random-phase approximation and the adiabatic time-dependent local-density approximation, and further confirmed with a simple slab model, allow us to argue that the above properties, being exceptional in the three-dimensional case, are common to quasi-two-dimensional systems.

cond-mat.mes-hall↗

arXiv2015

Electronic excitations in quasi-2D crystals: What theoretical quantities are relevant to experiment?

The ab initio theory of electronic excitations in atomically thin [quasi-two-dimensional (Q2D)] crystals presents extra challenges in comparison to both the bulk and purely 2D cases. We argue that the conventionally used energy-loss function $-$Im $1/ε({\bf q},ω)$ (where $ε$, ${\bf q}$, and $ω$ are the dielectric function, the momentum, and the energy transfer, respectively) is not, generally speaking, the suitable quantity for the interpretation of the electron-energy loss spectroscopy (EELS) in the Q2D case, and we construct different functions pertinent to the EELS experiments on Q2D crystals. Secondly, we emphasize the importance and develop a convenient procedure of the elimination of the spurious inter-layer interaction inherent to the use of the 3D super-cell method for the calculation of excitations in Q2D crystals. Thirdly, we resolve the existing controversy in the interpretation of the so-called $π$ and $π+σ$ excitations in monolayer graphene by demonstrating that both dispersive collective excitations (plasmons) and non-dispersive single-particle (inter-band) transitions fall in the same energy ranges, where they strongly influence each other.

cond-mat.mes-hall↗