Parabolic Potential Barrier Research Articles

Transition Path Dynamics of Non-Markovian Systems across a Rough Potential Barrier.

Transition paths refer to rare events in physics, chemistry, and biology where the molecules cross barriers separating stable molecular conformations. The conventional analysis of the transition path times employs a diffusive and memoryless transition over a smooth potential barrier. However, it is widely acknowledged that the free energy profile between two minima in biomolecular processes is inherently not smooth. In this article, we discuss a theoretical model with a parabolic rough potential barrier and obtain analytical results of the transition path distribution and mean transition path times by incorporating absorbing boundary conditions across the boundaries under the driving of Gaussian white noise. Further, the influence of anomalous dynamics in rough potential driven by a power-law memory kernel is analyzed by deriving a time-dependent scaled diffusion coefficient that coarse-grains the effects of roughness, and the system's dynamics is reduced to a scaled diffusion on a smooth potential. Our theoretical results are tested and validated against numerical simulations. The findings of our study show the influence of the boundary conditions, barrier height, barrier roughness, and memory effect on the transition path time distributions in a rough potential, and the validity of the scaling diffusion coefficient has been discussed.

Influence of Quantum Effects on Dielectric Relaxation in Functional Electrical and Electric Energy Elements Based on Proton Semiconductors and Dielectrics

Using the quasi-classical kinetic theory of dielectric relaxation, in addition to existing methods, fundamental mathematical expressions are built, which make it possible to more strictly consider the effects of the main charge carriers’ (protons’) tunneling on the numerical values of the molecular parameters (activation energy, equilibrium concentration) of protons in HBC. The formulas for calculating the statistically averaged non-stationary quantum transparency of a parabolic potential barrier for protons have been modernized by more stringent consideration of the effects of corrections caused by an external electric field. For the model of a double-symmetric potential well, a generalized nonlinear solution of the quasi-classical kinetic equation of dielectric relaxation in HBC was built. The phenomenological Bucci-Rive formula for thermally stimulated depolarization current density (TSDC) was first investigated, taking into account quantum transparency, for the case of a parabolic potential barrier. The choice of the parabolic shape of the potential barrier allowed, at a theoretical level, for the mathematical model of relaxation polarization to be brought closer to the conditions of the real spatial structure of the crystal potential field, in comparison with the rectangular potential barrier model. It has been found that quantum effects due to proton tunnel transitions significantly affect the mechanism of thermally stimulated depolarization currents in HBC, over a wide temperature range (50–550 K) and external field parameters (0.1–1 MV/m). Generalized solutions of the nonlinear kinetic equation, recorded considering the effects of field parameters on proton tunnel transitions, made it possible to significantly approximate the theoretical values of activation energies, equilibrium concentrations of protons and amplitudes of the theoretical maxima of the current density of thermally stimulated depolarization, according to their experimental values in the field of low-temperature (50–100 K) and high-temperature (350–550 K) maxima of TSDC density in HBC. For the first time, precision measurements of TSDC temperature spectra were carried out for chalcanthite crystals. The effects of alloying impurities concentrations and crystal calcination temperatures on the parameters of experimental maxima in the TSDC spectrum of chalcanthite were established. A physical mechanism of the quantum tunnel motion of protons in HBC with a complex crystal structure (crystalline hydrates, layered silicates, ferroelectric HBC (KDP, DKDP)) is described. The patterns found in this article indicate a fairly high degree of applied scientific significance for the obtained theoretical results, allowing for the further development of electrophysics and optoelectronics of heterogeneous structures (MIS, MSM) based on proton semiconductors and dielectrics (PSD) and their composites.

Nonlinear Quantum Phenomena During the Polarization of Nanometer Layers of Proton Semiconductors and Dielectrics

This paper investigates the influence of the structure and parameters of the degenerate quasi-discrete energy spectrum of relaxers (protons) on the mechanism of nonlinear quantum diffusion polarization in nanoscale layers of hydrogen bonded crystals (HBC) in a wide range of parameters of fields (100 kV/m - 1000 MV/m) and temperatures (0-1550 K). The temperature dependence of the quantum transparency of the parabolic potential barrier for protons in HBC is calculated using the Gibbs quantum canonical distribution for the ensemble of non-interacting protons (ideal proton gas balanced with the ions of anion sub-lattice) moving in an onedimensional potential field of a crystalline lattice (in the field of hydrogen bonds) with a zone structure distributed by energy levels. The influence of "zero" oscillations of protons on the temperature dependences of the proton subsystem kinetic coefficients in HBC is considered. It is revealed that proton tunneling influences the nonlinear space-charge polarization kinetics in HBC at high (150-550 K) and ultrahigh (550-1550 K) temperatures when crystalline layer thickness ranges from 1 to 10 nm. The results of theoretical studies (based on earlier experiments) are bound to be prospective for the prediction of HBC-class (KDP, DKDP) ferroelectrics properties, studying the second-order nonlinear optical effects of femtosecond lasers, and the development of memory cells for non-volatile high-speed memory devices.

Reactive flux theory for finite potential barriers.

Motivated by developing a simple, accurate, and widely applicable approach to incorporate the finite barrier correction in analytical calculation of the escape rate, the reactive flux theory for finite barriers is proposed. For higher temperatures, instead of at the top of the barrier in the original reactive flux theory, the starting point of the trajectories of Brownian particles is removed into a position inside the potential well where the probability distribution can be regarded as an equilibrium one, and the potential barrier is replaced with an equivalent parabolic potential barrier. The equivalent potential barrier frequency can be obtained by two schemes. The population is also calculated more realistically for finite barriers. The theoretical method is tested by a Brownian particle moving in a cubic metastable potential and subjected to Gaussian white noise. The numerical simulation results confirm the approach satisfactorily until lower reduced barrier heights.

Transition path dynamics across rough inverted parabolic potential barrier

Transition path dynamics have been widely studied in chemical, physical, and technological systems. Mostly, the transition path dynamics is obtained for smooth barrier potentials, for instance, generic inverse-parabolic shapes. We here present analytical results for the mean transition path time, the distribution of transition path times, the mean transition path velocity, and the mean transition path shape in a rough inverted parabolic potential function under the driving of Gaussian white noise. These are validated against extensive simulations using the forward flux sampling scheme in parallel computations. We observe how precisely the potential roughness, the barrier height, and the noise intensity contribute to the particle transition in the rough inverted barrier potential.

Nonlinear Polarization Effects in Dielectrics with Hydrogen Bonds

Using quasiclassical kinetic theory, nonlinear phenomena under the formation of space-charge polarization in crystals with hydrogen bonds (HBC) are investigated. From the solution of the nonlinear system of Fokker-Planck and Poisson equations with blocking electrodes, it is established that for the mathematical description of the relaxation polarization in HBCs in weak fields (100-1000 kV/m) and at high temperatures (T> 350 K), it is sufficient to use a linear approximation of perturbation theory. Theoretically, it was found that at the first odd frequency of the alternating field, nonlinear effects caused by the interaction of relaxation modes of various frequency orders start to appear. The diffusion and mobility coefficients are calculated taking into account both mechanisms of the protons transitions (thermally activated and tunneling transitions) through a parabolic potential barrier. A recurrence expression is constructed for calculating complex amplitudes of relaxation modes generated at an arbitrary frequency (multiple to the fundamental frequency) of the alternating field in an arbitrary approximation of perturbation theory. The proposed scheme for solving the kinetic equation can be applied to other crystals with ionic conductivity similar to HBCs in the type and properties of the crystal lattice.

Sensitivity of metal oxide gas sensors to non-parabolic intergranular barriers

We analyze the electrical conductivity of polycrystalline semiconductor solids due to the presence of Schottky-type potential barriers formed at intergrains. The density of charged dopants along the grains is usually considered constant leading to parabolic intergranular potential barriers. If temperature is high enough to allow sufficiently mobility to the dopants, their resulting equilibrium distribution is far from constant leading to potential barriers that show a strong non-parabolic character. Implications for the electrical conductivity and then on the sensitivity to barrier height and sample doping in metal oxide gas sensors are discussed.

Erratum: Quantization of unstable linear scalar fields in static spacetimes [Phys. Rev. D 88 , 124005 (2013)

We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a stationary external scalar potential. In order to prove our results we assume spacetimes without horizons and that the theory possess a "mass gap." Our strategy consists in building a complex structure, which arises from a suitable positive bilinear form defined over the space of classical solutions of the field equation. Once the space of states of the quantum field has been set, it is possible to study the effect of the time translation symmetry on it. From the time translation operator we obtain an expression for the Hamiltonian operator associated with the unstable sector of the field. This last result coincides with findings from long ago showing that the unstable degrees of freedom of the field behave as non-relativistic particles in a parabolic potential barrier.

Absorption coefficient and relative refractive index change for a double δ-doped GaAs MIGFET-like structure: Electric and magnetic field effects

In this work we present theoretical results for the electronic structure as well as for the absorption coefficient and relative refractive index change for an asymmetric double δ-doped like confining potential in the active region of a Multiple Independent Gate Field Effect Transistor (MIGFET) system. We model the potential profile as a double δ-doped like potential profile between two Schottky (parabolic) potential barriers that are just the main characteristics of the MIGFET configuration. We investigate the effect of external electromagnetic fields in this kind of quantum structures, in particular we applied a homogeneous constant electric field in the growth direction z as well as a homogeneous constant magnetic field in the x-direction. In general we conclude that by applying electromagnetic fields we can modulate the resonant peaks of the absorption coefficient as well as their energy position. Also with such probes it is possible to control the nodes and amplitude of the relative refractive index changes related to resonant intersubband optical transitions.

Quantization of unstable linear scalar fields in static spacetimes

We discuss the quantization of an unstable field through the construction of a ``one-particle Hilbert space.'' The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a stationary external scalar potential. In order to prove our results we assume spacetimes without horizons and that the theory possess a ``mass gap.'' Our strategy consists in building a complex structure, which arises from a suitable positive bilinear form defined over the space of classical solutions of the field equation. Once the space of states of the quantum field has been set, it is possible to study the effect of the time translation symmetry on it. From the time translation operator we obtain an expression for the Hamiltonian operator associated with the unstable sector of the field. This last result coincides with findings from long ago showing that the unstable degrees of freedom of the field behave as nonrelativistic particles in a parabolic potential barrier.

Sudden transition from a stable to an unstable harmonic trap as the adiabatic potential parameter is varied in a time-periodic harmonic trap

It has been shown already that when the harmonic trap is opened (or closed) as a function of time while keeping the adiabatic parameter $\ensuremath{\mu}=[d\ensuremath{\omega}(t)/dt]/{\ensuremath{\omega}}^{2}(t)$ fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at $\ensuremath{\mu}=2$ [Uzdin, Dalla Torre, Kosloff, and Moiseyev, Phys. Rev. A 88, 022505 (2013)]. Here we show that by using time-dependent linear coordinate transformation the time-dependent Schr\odinger equation with Hermitian time-dependent Hamiltonian is transformed into a time-dependent Schr\odinger equation with a time-independent harmonic oscillator with the dimensionless frequency of $\sqrt{1\ensuremath{-}{(\ensuremath{\mu}/2)}^{2}}$. At $\ensuremath{\mu}=2$ a transition to a non-Hermitian Hamiltonian is obtained as the potential well is transformed to a parabolic potential barrier. While in a harmonic trap noninteracting particles have classical periodic motions, they are pushed apart exponentially in time as the potential well is suddenly transformed into a parabolic potential barrier in the new variable representation.

Temperature dependence of interband recombination energy in symmetric (In,Ga)N spherical quantum dot-quantum well

Within the framework of effective-mass approximation and finite parabolic potential barrier, single particle and ground-state interband recombination energies in Core│well│shell based on GaN|(In,Ga)N|GaN spherical QDQW are investigated as a function of the inner and the outer radii. The temperature dependency of effective-mass, band-gap energy and potential barrier is taken into account. Particle eigenvalue and band-gap energy competing effects are speculated to explain our numerical results which show that the interband recombination energy increases when the temperature increases. The results we obtained are in quite good agreement with the findings.

Electron-hole transition in spherical QD-QW nanoparticles based on GaN∣(In,Ga)N∣GaN under hydrostatic pressure

Within the framework of effective-mass approximation and finite parabolic potential confinement barrier in which two confinement parameters are taking account, the electron (hole) energy and the ground-state electron-hole (e−h) transition in Core∣well∣shell (GaN|InxGa1−xN|GaN) spherical QD-QW nanoparticles are investigated as a function of the inner and the outer radii under externally applied hydrostatic pressure. The pressure dependencies of the effective-mass and the QD radius are taking into account. The results we obtained are in quite good agreement with the theoretical and the experimental findings.

Coherent states of inverse oscillators and related problems

We consider an example of a quantum system with a continuous and unbounded spectrum—a particle in the parabolic potential barrier. Conditionally, we call this system the inverse oscillator. Following the method used in our previous publication (Bagrov et al 2012 J. Phys. A: Math. Theor. 45 125306), we construct different families of generalized coherent states (GCS). We discuss properties of the constructed GCS and their relation to what is already known in the literature about semiclassical states for the inverse oscillator. Then in the same manner, we construct families of GCS for the normal oscillator. Using special variables, we succeeded in constructing GCS for the normal oscillator that admit different limiting cases: free particle GCS, the usual Schrödinger, Glauber CS and GCS of the inverse oscillator.

Uncorrelated electron-hole transition Energy in GaN│InGaN│GaN Spherical QDQW Nanoparticles

The electron (hole) energy and uncorrelated \(1S_e - 1S_{h}\) electron-hole transition in Core(GaN)| well(In\(_x\)Ga\(_{1 - x}\)N)| shell(GaN) spherical QDQW nanoparticles is investigated as a function of the inner and the outer radii. The calculations are performed within the framework of the effective-mass approximation and the finite parabolic potential confinement barrier in which two confined parameters are taking account. The Indium composition effect is also investigated. A critical value of the outer and the inner ratio is obtained which constitutes the turning point of two indium composition behaviors.

Hartman effect and dissipative quantum systems

The dwell time for dissipative quantum system is shown to increase with barrier width. It clearly precludes Hartman effect for dissipative systems. Here calculation has been done for inverted parabolic potential barrier.

Evaluation by tunneling effect for the temperature-dependent electric conductivity of polymer-carbon fiber composites with visco-elastic properties

The conductivity of composites with a carbon fiber (CF) content slightly higher than the percolation threshold was measured at increasing temperatures up to −10 °C. The tunneling effect was theoretically calculated using a rigorous nonparabolic potential barrier. The tunneling barrier width D and the surface area A were determined. For a polyethylene (PE) matrix, good agreement between theoretical and experimental results was obtained using D=1.00 nm and A=1.35 to 1.68 nm2 at a 30-vol% CF content and using D=1.30 nm and A=1.25 to 1.28 nm2 at a 25-vol% CF content. That is, almost perfect agreement between experiment and theory was obtained by adjusting the parameters except over the temperature ranges in which the β and γ relaxation peaks appeared. Dynamic loss modulus and positron annihilation measurements were also conducted. However, a theoretical analysis that was derived using a parabolic potential barrier produced inconsistent results. That is, the tunneling barrier width D was less than the c-axis length of a PE crystal unit, and the surface area A was considerably less than the a-b plane area of a PE crystal unit.

Quantum statistical effects in nuclear reactions, fission, and open quantum systems

Quantum diffusion equations with time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytical formulas for calculating friction and diffusion coefficients in nuclear processes are obtained. The asymptotics of the transport coefficients and of the correlation functions are investigated. The problem of correlation decay in quantum dissipative systems is studied. A comparative analysis of diffusion coefficients for the harmonic and inverted oscillators is performed. The role of quantum statistical effects during passage through a parabolic potential barrier is investigated. Sets of diffusion coefficient assuring the purity of states at any time instant are found in cases of non-Markovian dynamics. The influence of different sets of transport coefficients on the rate of decay from a metastable state is studied in the framework of the master equation for reduced density matrices describing open quantum systems. The approach developed is applied to investigation of fission processes and the processes of projectile-nuclei capture by target nuclei for bombarding energies in the vicinity of the Coulomb barrier. The influence of dissipation and fluctuation on these processes is taken into account in a self-consistent way. The evaporation residue cross sections for asymmetric fusion reactions are calculated from the derived capture probabilities averaged over all orientations of the deformed projectile and target nuclei.

On the Mean Free Path for Backscattering in $k_{B}T$ Layer of Bulk Nano-MOSFETs

We perform Monte Carlo particle simulations on a silicon conductor for the purposes of reexamining the channel backscattering in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bulk</i> nano-MOSFETs. The resulting mean free path lambda <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> for backscattering in a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long</i> and near-equilibrium conductor is constant, regardless of the potential profile. However, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">apparent</i> mean free path lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> in a local quasi-ballistic <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kBT</i> layer depends on the curvature of the potential profile. In a linear potential profile, the lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> extracted in a wide range of the conductor length (15 to 100 nm) and lattice temperature (150 to 300 K) is found to fall below lambda <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> . The carrier heating as the origin of reduced mean free path is inferred from the simulated carrier velocity distribution near the injection point. Strikingly, the mean free paths in a parabolic potential profile remain consistent: lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = lambda <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> . This indicates the absence or weakening of the carrier heating in the layer of interest, valid only for the parabolic potential barrier.

Light Propagation in Chiral Media with Large Pitch

The peculiarities of light propagation in uniaxial chiral media with large pitch are studied. In this case there are the forbidden zones for extraordinary beams. The existence of the forbidden zones leads to the effective reflection on zones boundaries and to damping of the wave inside the forbidden zone. We analyze the vicinities of the turning points and the transition of an extraordinary wave through the forbidden zone. It is shown that the optical effects for beams propagating near the turning points are equivalent to the tunnelling and reflection above the barrier for the parabolic potential barrier in quantum mechanics.