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We analyze various limits of vibrationally coupled resonant electron transport in single-molecule junctions. Based on a master equation approach, we discuss analytic and numerical results for junctions under a high bias voltage or weak…
The problem of the low-energy highly-anharmonic quantum dynamics of isolated impurities in solids is addressed by using path-integral Monte Carlo simulations. Interstitial oxygen in silicon is studied as a prototypical example showing such…
We compute the quasi-bound state spectra of ultralight scalar and vector fields around rotating black holes. These spectra are determined by the gravitational fine structure constant $\alpha$, which is the ratio of the size of the black…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
The excess low-frequency normal modes for two widely-used models of glasses were studied at zero temperature. The onset frequencies for the anomalous modes for both systems agree well with predictions of a variational argument, which is…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
We calculated the dynamics of nuclear wave packets in coupled electron-vibration systems and their nonlinear optical responses. We found that the quantized nature of the vibrational modes is observed in pump-probe spectra particularly in…
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the…
There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, "hyperbolic". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption,…
In this paper we study semiclassical states for the problem $$ -\eps^2 \Delta u + V(x) u = f(u) \qquad \hbox{in} \RN,$$ where $f(u)$ is a superlinear nonlinear term. Under our hypotheses on $f$ a Lyapunov-Schmidt reduction is not possible.…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…
In the paper are considered stationary (Bloch) states of a particle, in the field of periodic biparabolic type potential. It is shown that while the particle's energy decreases in limits of a single energy band, the probability of the…
The nonrelativistic variational calculation of a complete set of ro-vibrational states in the H$_2^+$ molecular ion supported by the ground $1s\sigma$ adiabatic potential is presented. It includes both bound states and resonances located…
We consider model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a periodic excitation is considered. It is shown that…
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system, and argue that it offers lessons for real molecular collisions in…
In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of…
The dynamics of active matter driven by interacting molecular motors has a non-potential structure at the local scale. However, we show that there exists a quasi-potential effectively describing the collective self-organization of the…
Dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, is considered by applying an accurate method for solving nonlinear systems of differential equations. This method is more general than the…
A close inspection of neutron spectra of glass formers in the frequency region above the boson peak does not show the constant eigenvalue density expected for a random dynamical matrix, but a slow decrease towards higher eigenvalues. In…
The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be…