Gaussian wavepacket dynamics and quantum tunneling in asymmetric double-well systems

Gaussian wavepacket dynamics in an anharmonic system

We find a relationship between the dynamics of the Gaussian wave packet and the dynamics of the corresponding Gaussian Wigner function from the Hamiltonian/symplectic point of view. The main result states that the momentum map corresponding to the natural action of the symplectic group on the Siegel upper half space yields the covariance matrix of the corresponding Gaussian Wigner function. This fact, combined with Kostant’s coadjoint orbit covering theorem, establishes a symplectic/Poisson-geometric connection between the two dynamics. The Hamiltonian formulation naturally gives rise to corrections to the potential terms in the dynamics of both the wave packet and the Wigner function, thereby resulting in slightly different sets of equations from the conventional classical ones. We numerically investigate the effect of the correction term and demonstrate that it improves the accuracy of the dynamics as an approximation to the dynamics of expectation values of observables.

The tunneling probability for majority carriers in an ohmic contact to n-type GaAs has been calculated by directly solving the Schrödinger equation for the wave functions in the semiconductor depletion region. The direct solution is straightforward and relies on fewer assumptions than previous calculations based on the WKB approximation. It also provides a useful application of undergraduate quantum mechanics to an important area of VLSI semiconductor technology. The direct solution can be performed on an 80286 machine in less than a minute and yields tunneling probabilities roughly twice as large as the WKB approximation at most electron energies. The tunneling probability is then used to calculate the contact resistance as a function of doping for the contact. The contact resistances are approximately one-half the resistances calculated using the WKB method.

Multiple experiments on the electron transport through solid-state junctions based on different proteins have suggested that the dominant transport mechanism is quantum tunneling (or coherent transport). This is extremely surprising given the length of these molecules (2–7 nm) and their electronic structure (mainly comprising very localized molecular orbitals). Overall, this is probably the single most important puzzle in the field of biomolecular electronics and calls for rigorous calculations of the tunneling probability in protein-based junctions. Motivated by these experiments, we tackle here this problem and report a comprehensive theoretical study of the coherent electron transport in metal–protein–metal junctions based on the blue-copper azurin from Pseudomonas aeruginosa, which is the workhorse in protein electronics. More precisely, we focus on single-molecule junctions realized in STM-based experiments and analyze a wide variety of contact scenarios. Our calculations are based on a combination of molecular dynamics simulations and ab initio transport calculations. Our results unambiguously show that when azurin is not deformed and retains its pristine structure, the end-to-end tunneling probability is exceedingly small and does not give rise to any measurable electrical current. On the other hand, we find that much higher tunneling probabilities are possible when either the STM tip (indented from the top) substantially compresses the protein or the protein is contacted sideways, significantly reducing the effective junction length. We also show that in certain configurations, the presence of surrounding water can also increase the conductance but it cannot explain the high conductance values reported experimentally. In all cases, the current is found to flow through the Cu atom of this metalloprotein, although the role of several other levels close to the Fermi energy cannot be ruled out. We remark that we only evaluate the efficiency of coherent transport and the analysis of the relevance of other potential charge-transport mechanisms is out of the scope of our work.

We review our comprehensive investigations of electron and hole tunneling times between quantum wells separated by a single barrier. These studies show strong electronic and phonon resonances, strong influence of collisions and relaxation on tunneling times and provide new insights into nonresonant and resonant tunneling in semiconductor microstructures.

Second Moment of an NMR Spectrum of a Solid Narrowed by Molecular Jumps in Potential Wells with Nonequivalent Sites

The dynamics of collinear exchange reactions is treated within a semiclassical Gaussian wave packet (GWP) description. Two extensions to the previous methodology of GWP dynamics are presented. The first involves the evaluation of the interaction picture wave function propagators directly via the GWP solution to the time-dependent Schrödinger equation. The second involves use of a sum of GWPs to represent the initial translational plane wave on a finite interval. As usual, the vibrational wave function is also represented as a sum of GWPs, where the expansion coefficients are chosen to yield the desired initial vibrational state. The limitations of the previous GWP dynamical methods as applied to the reactive scattering problem are pointed out and the solutions provided by the present extensions are discussed. Results for the H+H2 collinear exchange reaction using the Porter–Karplus II potential energy surface are shown.

Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle exhibits quantum-like behavior: complex-energy classical particles can travel between classically allowed regions separated by potential barriers. When Im E → 0, the classical tunneling probabilities persist. Hence, one can interpret quantum tunneling as an anomaly. A numerical comparison of complex classical tunneling probabilities with quantum tunneling probabilities leads to the conjecture that as Re E increases, complex classical tunneling probabilities approach the corresponding quantum probabilities. Thus, this work attempts to generalize the Bohr correspondence principle from classically allowed to classically forbidden regions.

Local electric field effects in a SiGe quantum well investigated by photoluminescence

Efficiently collecting ambient vibrations has been the research hotspot of energy harvesting technology. In this paper, an asymmetric bi-stable energy harvester is proposed to tune the bandwidth as well as to enhance the output power. By only shifting the magnet positions from symmetric to asymmetric, and requiring no ancillary mechanical structures, asymmetric double potential wells can be constructed, working bandwidth can be extended, and average output power can be increased by 10.2%. Maximally, the asymmetric bi-stable energy harvester prototype generates root mean square voltage of 3.173V on 90.5MΩ resistance @9.5Hz excitation.

The electrostatic potential well in an inertial-electrostatic confinement (IEC) is calculated by performing the numerical simulations based on the particle-in-cell method. The single, double and triple wells, depending on the amount of the injected ion current, are observed to be formed for the ions with a mono-energetic distribution. The well in the center of the multi-well structure is unstable and oscillates at the period much longer than the ion plasma frequency. A double well structure can be formed even for the ions with a spread energy distribution when the ion current is larger than the threshold value. The time-averaged neutron production in D-D fusion events is found to be proportional to the third power of the ion current where the double well structure is formed. The numerical simulation reveals that an IEC possesses the favorable dependence of fusion reactions on the injected ion current for the application to a neutron source or a fusion reactor.

Linear and nonlinear optical absorption coefficients and refractive index changes in asymmetrical Gaussian potential quantum wells with applied electric field

Electron tunneling through single barriers, taking into account the coupling between two different band-edge profiles, is studied by means of a heuristic two-band tight-binding model. The tunneling probabilities, as well as the spectral weights of the tunneling states, are analyzed. This indirect-barrier system directly addresses the issue of \ensuremath{\Gamma}-X coupling in GaAs-(Al,Ga)As heterostructures. A relation between this physical system and the resonant tunneling through double-barrier quantum wells and also the atomic-potential scattering is established. The nature of the resonances in the transmission probabilities is discussed and it is shown under which conditions the shape of these resonances can change.

Potential well evolution and metastable dynamics of bistable asymmetric laminated composite square shallow shell under external and parametric excitations

The effects of coupling to a harmonic oscillator on the quantum tunneling of a macroscopic motion are studied through the influence functional formalism of Feynman's path integral method for the general coupling form factor. As an example, we consider the model in which the potential barrier is parabolic and the coupling Hamiltonian is linear in both coordinates of the macroscopic motion and of the intrinsic harmonic oscillator. The results are then compared with the exact solution obtained through the canonical transformation into normal coordinates in the limiting cases when the normal coordinates reduce to the original coordinates. We found that: (1) In the adiabatic case, i.e., when the recurrence time $\frac{\ensuremath{\pi}}{\ensuremath{\omega}}$ of the oscillator is much shorter than the transmission time through the macroscopic potential barrier, the effect of oscillator coupling can be well represented by an effective potential. The coupling enhances the tunneling probability on the whole. (2) There exists a critical energy, above which the tunneling probability is reduced because of the linear oscillator coupling. In the weak coupling limit and when $\ensuremath{\omega}\ensuremath{\rightarrow}0$, the critical energy becomes $\ensuremath{-}\ensuremath{\infty}$, so that the coupling to the oscillator always reduces the tunneling probability.NUCLEAR REACTIONS Quantum tunneling, coupling of macroscopic motion to intrinsic oscillators, semiclassical method, heavy ion fusion.