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We consider simple models of tunneling of an object with intrinsic degrees of freedom. This important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. We show possibilities of enhancement for the probability of tunneling due to the presence of intrinsic degrees of freedom split by weak external fields or by polarizability of the slow composite object.Quantum tunneling is a subject of constantly renewed interest, both experimentally and theoretically. The standard textbook approach describes the tunneling process for a point-like particle in an external static potential. Chemical and nuclear subbarrier reactions [1], especially in astrophysical conditions, as a rule, involve complex objects with their intrinsic degrees of freedom. As stated in Ref. [2], "Although a number of theoretical works have studied tunneling phenomena in various situations, quantum tunneling of a composite particle, in which the particle itself has an internal structure, has yet to be clarified." There are experimental data [3,4] indicating that at low energies the penetration probability for loosely bound systems, such as the deuteron, can noticeably exceed the conventional estimates.The problems of tunneling and reflection of a composite particle were discussed recently with the help of various models [5,6,7,8,9,10,11]. It was stressed that new, usually ignored, effects are important for nuclear fusion and fission, nucleosynthesis in stars, molecular processes, transport phenomena in semiconductors and superconductors, both in quasi-one-dimensional and three-dimensional systems. The resonant tunneling associated with the intrinsic excitation, finite size effects, polarizability of tunneling objects, evanescent modes near the barrier, real [12,13] and virtual [14] radiation processes are the examples of interesting new physics. Below we consider simple models which illustrate how "hidden" degrees of freedom can show up in the process of tunneling leading to a considerable enhancement of the probability of this process.Let the tunneling particle possess two degenerate intrinsic states and the incident wave comes to the barrier in a pure state "up" (it is convenient to use the spin-1/2 language with respect to the z-representation). We assume one-dimensional motion with the simplest rectangular potential barrier of height U 0 located at 0 < x < a. At low energy E ≪ U 0 , when the imaginary action κ 0 a = [2m(U 0 − E)] 1/2 a is very large, the transmission coefficient T 0 ∝ exp(−2κ 0 a) is exponentially small. This probability can be exponentially enhanced by a weak "magnetic" field applied in the area of the barrier. We assume that the interaction of this field with the particle is −hσ x , where h is proportional to the transverse magnetic field.Indeed, this field creates the "down" spin component and splits the states inside the barrier according to the value of σ x . In the z-representation the regions x ≤ 0 and x ≥ a acquire the down component in the reflected a...

Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the unitarity of the scattering matrix. The intrinsic interaction is modelled by the two-body random ensemble of variable strength. In particular, the crossover region from isolated to overlapping resonances accompanied by the effect of the width redistribution creating super-radiant and trapped states is studied in detail. The important observables, such as average cross section, its fluctuations, autocorrelation functions of the cross section and scattering matrix, are very sensitive to the coupling of the intrinsic states to the continuum around the crossover. A detailed comparison is made of our results with standard predictions of statistical theory of cross sections, such as the Hauser-Feshbach formula for the average cross section and Ericson theory of fluctuations and correlations of cross sections. Strong deviations are found in the crossover region, along with the dependence on intrinsic interactions and degree of chaos inside the system.

We study the bremsstrahlung radiation of a tunneling charged particle in a time-dependent picture. In particular, we treat the case of bremsstrahlung during alpha-decay, which has been suggested as a promissing tool to investigate the problem of tunneling times. We show deviations of the numerical results from the semiclassical estimates. A standard assumption of a preformed particle inside the well leads to sharp high-frequency lines in the bremsstrahlung emission. These lines correspond to "quantum beats" of the internal part of the wavefunction during tunneling arising from the interference of the neighboring resonances in the well.

Using the phenomenological expression for the level spacing distribution with only one parameter, 0 ≤ β ≤ ∞, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between β and the normalized localization length for the whole transition from strongly localized to extended states. This result allows one to describe all transport properties in the open system entirely in terms of the parameter β and strength of coupling to continuum. For non-perfect coupling, our data show a quite unusual interplay between the degree of internal chaos defined by β, and degree of openness of the model. The results can be experimentally tested in single-mode waveguides with either bulk or surface disorder.

We study the statistical properties of resonance widths and spacings in an open system of interacting fermions. At the transition between isolated and overlapping resonances, a radical change in the width distribution occurs with segregation of broad ("super-radiant") and narrow ("trapped") states. Our main interest is to reveal how this transition is influenced by the onset of chaos in the internal dynamics regulated by the strength of random two-body interaction. In the transitional region, the width distribution and its variance, as well as the distribution of spacings between resonances are strongly affected by internal chaos. The results may be applied to the analysis of neutron cross sections, as well as in the physics of mesoscopic devices with strongly interacting electrons.