Two-dimensional tunnel correlations with dissipation

Abstract

Tunneling of two particles in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. The critical temperature T_c corresponding to a bifurcation of the underbarrier trajectory is determined. The effect of a heat bath local mode on the probability of two-dimensional tunneling transfer is also investigated. At certain values of the parameters, the degeneracy of antiparallel tunneling trajectories is important. Thus, four, six, twelve, etc., pairs of the trajectories should be taken into account (a cascade of bifurcations). For the parallel particle tunneling the bifurcation resembles phase transition of a first kind, while for the antiparallel transfer it behaves as second order phase transition. The proposed theory allows for the explanation of experimental data on quantum fluctuations in two-proton tunneling in porphyrins near the critical temperature.Comment: RevTeX4, twocolumn, 12 pages, 11 figures (17 eps-files). Revised version, to appear in Phys. Rev.

A comparative analysis of the observed effects of 2D tunneling bifurcations for quasi-one-dimensional and quasi-two-dimensional Au–QD systems in an external electric field

“…The effect of 2D-tunneling bifurcations for the parallel transfer of interacting particles in the weak-dissipation limit with allowance for the quantum beat regime in the vicinity of the bifurcation point, predicted by us in an earlier work [1], has been observed experimentally in a quasi-one-dimensional Au-QD array in an external electric field by Conductive Atomic Force Microscopy (CAFM). A description of the relevant experiment is presented in Section 2 of this article [4].…”

Analytic structure and power series expansion of the Jost function for the two-dimensional problem

“…First of all, modern nano-technology allows us to fabricate the microscopic quantum devices that behave and can be described as one-or two-dimensional. The two-dimensional tunneling of particles play an important role in superconductive tunnel junctions and even in some biological molecules [1]. Besides that, the corresponding quantum mechanical problems are not mathematically simple as one may think.…”

Phonon assisted resonant tunneling and its phonons control

“…(1) p α are momenta of phonon modes of the particle of mass m = 1, y α are coordinates of local phonon modes, ω α are frequencies of local phonon modes, N is the number of local modes of wide-band matrix, and C α are coefficients of the interaction of the tunneling particle with local phonon modes of wide-band matrix (see [13,16,17] for more details). The quasiclassical action S{y 1 } of the system is defined by [16] S {y 1 } =…”

“…In particular, probability rate of quantum tunneling of two mutually interacting charged particles moving in medium, which occurs in synchronous or asynchronous modes, was studied in our previous work [16].…”

“…Physical and chemical approaches to electron transfer processes at nanoscales reveal some common tools. Namely, analytical models of multidimensional dissipative simultaneous quantum tunneling of one or two charged particles, electrons or protons, in low-dimensional systems used in studying some chemical reactions at low temperatures [6][7][8][9][10][11][12][13][14][15][16][17], can be used to study physical properties of quantum dots (QDs) [7], [18][19][20].…”