Dynamic and spectral mixing in nanosystems

In the framework of a simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir states are formed by three sequences with rationally independent periodicities 1; 1 ± δ typical for vibrational states in many nanosize systems (e.g., large molecules containing CH₂ fragment chains, or carbon nanotubes). We show that quantum evolution of the system is determined by a dimensionless parameter δΓ, where Γ is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. When δΓ > 1 spectral chaos destroys recurrence cycles and the system state evolution is stochastic-like. In the opposite limit δΓ < 1 dynamics is regular up to the critical recurrence cycle k _c and for larger k > k _c dynamic mixing leads to quasi-stochastic time evolution. Our semi-quantitative analytic results are confirmed by numerical solution of the equation of motion. We anticipate that both kinds of stochastic-like behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems in the spectral window 10¹¹–10¹³ s⁻¹     

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state S, coupled to all other intra-molecular vibrational states R of the same molecule, and also to its environment Q. Molecular states forming the first reservoir R are characterized by a discrete dense spectrum, whereas the environment reservoir Q states form a continuous spectrum. Assuming the equidistant reservoir R states we find the exact analytical solution of the quantum dynamic equations. S-Q and R-Q couplings yield to spontaneous decay of the S and R states, whereas S-R exchange leads to recurrence cycles and Loschmidt echo at frequencies of S-R transitions and double resonances at the interlevel reservoir R transitions. Due to these couplings the system S time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system S dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are possible four dynamic regimes of the evolution: (i) independent of the environment Q exponential decay suppressing backward R - S transitions, (ii) Loschmidt echo regime, (iii) incoherent dynamics with multicomponent Loschmidt echo, when the system state is exchanged its energy with many states of the reservoir, (iv) cycle mixing regime, when long time system dynamics looks as a random-like. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.     

Revivals in Caldeira–Leggett Hamiltonian dynamics

We reconsider the problem of quantum system interacting with a complex environment discussed by Caldeira and Leggett (CL), and generalize their results for a quantum oscillator coupled to a reservoir R with dense discrete spectrum of oscillators with close to ${\omega }_s$ frequencies. Dynamics consists of recurrence cycles with partial revivals of the initial state. This revival or Loschmidt echo appears in each cycle. Width and number of the Loschmidt echo components increase with the recurrence cycle number leading to irregular, stochastic-like time evolution.     

Chemomechanical Coupling of Molecular Motors: Thermodynamics, Network Representations, and Balance Conditions

Molecular motors are considered that convert the chemical energy released from the hydrolysis of adenosine triphosphate (ATP) into mechanical work. Such a motor represents a small system that is coupled to a heat reservoir, a work reservoir, and particle reservoirs for ATP, adenosine diphosphate (ADP), and inorganic phosphate (P). The discrete state space of the motor is defined in terms of the chemical composition of its catalytic domains. Each motor state represents an ensemble of molecular conformations that are thermally equilibrated. The motor states together with the possible transitions between neighboring states define a network representation of the motor. The motor dynamics is described by a continuous-time Markov process (or master equation) on this network. The consistency between thermodynamics and network dynamics implies (i) local and nonlocal balance conditions for the transition rates of the motor and (ii) an underlying landscape of internal energies for the motor states. The local balance conditions can be interpreted in terms of constrained equilibria between neighboring motor states; the nonlocal balance conditions pinpoint chemical and/or mechanical nonequilibrium.     

Dissipative tunneling in nanosystems

A quantum dynamical problem has been analytically solved for a two-level system where localized states L ₀ and R ₀ are strongly coupled with reservoirs of local oscillations {L _n } and {R _n }. It is additionally assumed that the spectra of reservoirs are equidistant and the coupling constants are the same. It has been shown that the evolution of states L ₀ and R ₀ in recurrence cycles depends on three independent factors, which characterize exchange with the two-level system, exchange of L ₀ with {L _n } (R ₀ with {R _n }) and the phonon-induced decay of {L _n } and {R _n }. In addition to coherent oscillations with the frequency of the two-level system, Δ, and dissipative tunneling with a rate Δ²/πC ² (where C is the matrix element of the coupling of L ₀ and R ₀ with L _n and R _n ), a new regime appears where L-R transitions are induced by the partial recovery of the populations of L ₀ and R ₀ in each recurrence cycle due to synchronous transitions from reservoirs. These transitions induce repeating changes in the populations of the states of the two-level system (Loschmidt echo). The number and width of the echo components increase with the cycle number. Evolution becomes irregular because of the mixing of the contributions from pulses of the neighboring cycles, when the cycle number k exceeds the critical value k _c = π² C ². Unlike the populations, their cycle-average values remain regular at k ≫ k _c. When Δ ≪ πC ², the cycle-average populations oscillate with a frequency of ΔΩ/πC ² irrespective of mixing. The frequency of oscillations of the populations of the states {L _n } and {R _n } is approximately nΩ(Δ/2πC ²)², where Ω is the spacing between the neighboring levels of the reservoir and nΩ is the difference between the energies of the states L ₀ and L _n . The appearance of the mentioned low-frequency oscillations is due to the formation of collective states of the two-level system that are “dressed” by the reservoir. The predicted oscillations can be detected by femtosecond spectroscopy methods.     

Bohr correspondence principle for large quantum numbers

Periodic systems are considered whose increments in quantum energy grow with quantum number. In the limit of large quantum number, systems are found to give correspondence in form between classical and quantum frequency-energy dependences. Solely passing to large quantum numbers, however, does not guarantee the classical spectrum. For the examples cited, successive quantum frequencies remain separated by the incrementhI ^?1, whereI is independent of quantum number. Frequency correspondence follows in Planck's limit,h → 0. The first example is that of a particle in a cubical box with impenetrable walls. The quantum emission spectrum is found to be uniformly discrete over the whole frequency range. This quality holds in the limitn → ∞. The discrete spectrum due to transitions in the high-quantum-number bound states of a particle in a box with penetrable walls is shown to grow uniformly discrete in the limit that the well becomes infinitely deep. For the infinitely deep spherical well, on the other hand, correspondence is found to be obeyed both in emission and configuration. In all cases studied the classical ensemble gives a continuum of frequencies.     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

The Giant Dipole Resonance in the superdeformed143Eu nucleus

The γ-decay of the Giant Dipole Resonance (GDR) built on excited nuclear states has been measured for the nucleus¹⁴³Eu. The reaction¹¹⁰Pd(³⁷Cl, 4n)¹⁴³Eu at a beam energy of 165 MeV has been employed. This experiment aimed at searching the γ-decay of the GDR built on the superdeformed¹⁴³Eu states, populated at high spins. High-energy γ-rays were detected in 8 large BaF₂ scintillators in coincidence with discrete transitions measured with the NORDBALL array (in the configuration consisting of 17 HPGe detectors and a 2π multiplicity filter). The spectrum of high-energy γ-rays gated by low-energy transitions between states fed by the superdeformed states shows some excess of yield in the 7–10 MeV region with respect to that gated by transitions between states not populated by the superdeformed states. This excess should be due to the γ-decay of the the giant dipole oscillation along the superdeformed axis of the nucleus that is expected to have a frequency corresponding to ≈9–10 MeV (low-energy component of the GDR strength function). The measured excess, in spite of the large error bars, is found to be of the same order as predicted statistical model values.     

Charge-transfer transitions and optical spectra of vanadates

Specific features of the charge-transfer states and O2p → V3d transitions in the (VO₆)^9? octahedral complex are studied using the cluster approach. The reduced matrix elements of the electric-dipole transition operator are calculated for many-electron wave functions corresponding to the initial and final states of a charge-transfer transition. Using a parameterization of the results, the relative intensities of the allowed charge-transfer transitions are calculated disregarding the mixing of different configurations of the same symmetry. The Tanabe-Sugano theory is used with inclusion of this mixing to calculate the energies of many-electron charge-transfer transitions and their actual intensities. Modeling of the optical spectrum of LaVO₃ reveals a complicated charge-transfer transition band consisting of 81 lines. The main maxima of the band are in the range 6.3–7.3 eV. There are also additional maxima in the regions of ≈3 and ≈8–9 eV. The bandwidth is ≈10 eV. The results of model calculations are in agreement with experiments and demonstrate the weakness of the widely used assumption that the spectrum of charge-transfer transitions has a simple structure.     

Quantum dynamics of nanosystems with nonequidistant spectrum

A quantum problem of the evolution of a system coupled to a reservoir for which the interlevel spacing monotonically increases or decreases with increasing energy was solved. It was demonstrated that, despite the absence of an unambiguous definition of the recurrence cycle period, there is a wide range of parameters within which the basic feature of the evolution of system with an equidistant spectrum persist: the existence of the Loschmidt echo and mixing of the cycles that initiates the transition from a regular to a stochastic dynamic behavior. The results predict the existence of nonergodic nanosystems in which, as they evolve, energy periodically concentrates on certain vibrational degrees of freedom.     

Submillimeter wave spectrum and molecular constants of N2O

The submillimeter wave spectrum of the N₂O molecule has been investigated within the 375–565 GHz frequency range with a sensitivity better than 10^?8 cm^?1. The measured frequencies include 161 lines with intensities γ ? 10^?6 cm^?1 belonging to 22 spectroscopically different species of the molecule (specifically, the ground and some excited vibrational states of the five most abundant isotopic species of the molecule in natural abundance) with a statisticall and systematic error of the order of magnitude 10^?8. Rotational and two centrifugal stretching constants could be determined for each spectroscopic species. For each isotopic species observed, we have made a general analysis of the spectrum in different vibrational states bearing in mind resonance effects. The total number of the rotational and rovibrational constants obtained exceeds 40.     

Intramolecular vibrational dynamics of propyne and its derivatives: The role of vibrational-rotational mixing

The dynamics of intramolecular vibrational energy redistribution from the initially excited ν_HC mode in the propyne molecule (H-C≡C-CH₃), as well as in three its derivatives that are obtained by replacing one of the hydrogen atoms of the methyl group with the chlorine atom (propargylchloride), the OH radical (propargyl alcohol), or with the NH₂ radical (propargylamine), has been studied. Probing was performed by anti-Stokes spontaneous Raman scattering. The measured values of the deexcitation rate W of the ν_HC mode lie in the range 10⁹?10¹⁰ s^?1. A significant feature of the dynamics—an incomplete energy redistribution from the ν_HC mode—is especially clearly pronounced for the H-C≡C-CH₃ and H-C≡C-CH₂Cl molecules, for which the values of the relative level σ of the residual energy in the ν_HC mode are approximately equal to 0.54 and 0.25, respectively. A theoretical analysis performed made it possible to relate the parameters W and σ, on the one hand, and the density ρ of the so-called bath states, which are responsible for the vibrational energy redistribution, on the other hand. It is shown that, for all the four molecules considered, the required values of ρ can be accounted for solely by a strong vibrational-rotational mixing in the bath, as a result of which the projection of the total angular momentum onto the axis of the molecule ceases to be “good” quantum number.     

Fatigue of lead titanate and lead zirconate titanate thin films

The fatigue of lead titanate and lead zirconate titanate ferroelectric thin films, i.e., a change in the polarization as a function of the number of switching cycles in an external electric field, is investigated experimentally. The threshold numbers of switching cycles are determined to be 10¹⁰–10¹¹ for the lead titanate films and 10⁹–10¹⁰ for the lead zirconate titanate films. It is shown that a change in the temperature does not substantially affect the threshold number of switching cycles at which the switched polarization decreases drastically. However, an increase in the external field strength leads to a noticeable decrease in the threshold number of switching cycles. The process of fatigue is accompanied by an increase in the coercive field and the internal bias field. It is established that, as the number of switching cycles increases, the internal bias field changes more significantly as compared to the coercive field. The absence of a change in the phase composition in repeatedly switched samples indicates that the fatigue processes have a nonchemical nature. The anomaly observed in the frequency dependence of the permittivity in the frequency range 10⁶–10⁷ Hz due to the domain structure disappears after multiple switching cycles. This suggests that the observed fatigue phenomenon has a domain nature.     

The magnetic rotation spectrum of iodine monobromide

The MRS of IBr in the visible region of the spectrum has been studied at high resolution and a rotational and vibrational analysis is reported. The spectrum consists of short runs in J′ for several neighboring vibrational states of the mixed B, ${}^3\text{Π}{}_0{}^{\mathrm{+}}$, and $\text{B}\text{?}\text{′}$, 0⁺ electronic states. These results imply that only a small number of closely related rotational-vibrational states of the combined system have sufficiently long lifetimes to provide the sharp lines required for the appearance of a MRS. The values observed extend to higher energies similar results reported by Selin for the absorption spectrum.     

Kondo impurities in nanoscopic and mesoscopic systems

We present results for Kondo impurities in nanoscopic systems. Using Wilson's numerical renormalization group we analyze two different situations: an isolated system with a discrete spectrum of well-defined energy levels and a fixed number of electrons and a nanoscopic system weakly coupled to a macroscopic reservoir. In the latter case, new regimes not observed in macroscopic homogeneous systems are induced by the confinement of conduction electrons. These new confinement-induced regimes are very different depending on whether the Fermi energy is at resonance or between two quasi-bound states.     

Influence of temperature on tensile and fatigue behavior of nanoscale copper using molecular dynamics simulation

The tensile and fatigue behavior of nanoscale copper at various temperatures has been analyzed using molecular dynamics simulation. The stress–strain curve for nanoscale copper was obtained first and then the Young's modulus of the material was determined. The modulus was larger than that obtained by previous studies and decreased with increasing temperature. From the fatigue test, the cyclic stress–number of cycles curve was obtained and the stress increased with increasing temperature. Furthermore, the ductile fracture configuration was observed in the fatigue testing process under the lower applied stress. It was also observed that nanoscale copper appears to have a fatigue limit of 10⁵ cycles.     

Full Fermi–Pasta–Ulam Recurrence Interaction with Fluctuations of the Medium

It is shown in a numerical study that the simultaneous influence of discrete and continuous random processes on the full Fermi–Pasta–Ulam (FPU) recurrence dynamics in two parametrically coupled identical chains of vibrators with open ends and under different initial conditions leads to stabilization of the FPU spectrum. A greater influence on chains of gaussian noise as compared to discrete noise is revealed. An increase in the amplitudes of both noises by one order of magnitude results in considerable parameter changes in their FPU spectrum. The full FPU recurrence interaction in coupled chains with discrete and continuous random noise of the medium manifests itself in extremely low-frequency periodic processes in stochastic dynamics of the medium (with frequency two orders of magnitude lower than the lowest frequency in the initial conditions of the chains).     

Thermalization of Fermionic Quantum Walkers

We consider the discrete time dynamics of an ensemble of fermionic quantum walkers moving on a finite discrete sample, interacting with a reservoir of infinitely many quantum particles on the one dimensional lattice. The reservoir is given by a fermionic quasifree state, with free discrete dynamics given by the shift, whereas the free dynamics of the non-interacting quantum walkers in the sample is defined by means of a unitary matrix. The reservoir and the sample exchange particles at specific sites by a unitary coupling and we study the discrete dynamics of the coupled system defined by the iteration of the free discrete dynamics acting on the unitary coupling, in a variety of situations. In particular, in absence of correlation within the particles of the reservoir and under natural assumptions on the sample’s dynamics, we prove that the one- and two-body reduced density matrices of the sample admit large times limits characterized by the state of the reservoir which are independent of the free dynamics of the quantum walkers and of the coupling strength. Moreover, the corresponding asymptotic density profile in the sample is flat and the correlations of number operators have no structure, a manifestation of thermalization.