Publications

We introduce a general variational framework to address the tunneling of hot Fermi systems. We use the representation of the trace of the imaginary time τ=it propagator as a functional integral type of a sum over complete sets of states at intermediate propagation slices. We assume that these states are τ-dependent and generated by an arbitrary trial Hamiltonian H₀(τ). We then use the convexity inequality to derive H₀(τ) controlled variational bound for a trial action functional. This functional has a general structure consisting of two parts - statistically weighted quantum penetrability and dynamical tunneling entropy. We examine how this structure incorporates the basic physics of tunneling of hot Fermi systems. Using the variational inequality one can optimise the dynamical parameters controlling the action functional for any choice of the trial problem. As an application we take H₀(τ) to describe imaginary time dynamics of non interacting Bogoliubov-de Gennes (BdG) quasiparticles. Optimising its dynamical parameters we extend the tunneling theory of hot Fermi systems to the Hartree-Fock-Bogoliubov (HFB) frame and derive the corresponding generalisation of imaginary time temperature dependent BdG mean field equations. As in the trial action the prominent feature of these equations is an inseparable interplay between quantum dynamical and entropic statistical effects. In the zero temperature limit these equations describe the “false ground state” tunneling decay of superfluid Fermi systems (spontaneous fission in nuclear physics). With increasing excitation energy (effective temperature) the decay process is gradually evolving from pure quantum tunneling to statistical “bottle neck” escape mechanism. Correspondingly the statistically weighted dynamical penetrability part in the action gradually decreases while the tunneling entropy increases with increasing effective temperature.

Techniques to deal with Feshbach resonances are applied to describe resonant light scattering off one dimensional photonic crystal slabs. Accurate expressions for scattering amplitudes, free of any fitting parameter, are obtained for isolated as well as overlapping resonances. They relate the resonance properties to the properties of the optical structure and of the incident light. For the most common case of a piecewise constant dielectric function, the calculations can be carried out essentially analytically. After establishing the accuracy of this approach we demonstrate its potential in the analysis of the reflection coefficients for the diverse shapes of overlapping, interacting resonances.

We develop a path integral approach for analyzing the stationary light propagation in general dielectric media. The Hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle with spin-orbit coupling and position dependent mass. After appropriate ordering several path integral representations of a solution are constructed. First we keep the propagation of the polarization degrees of freedom in an operator form integrated over paths in a coordinate space. The use of spin 1 coherent states allows representing this part as a path integral over such states. Finally a path integral in a transversal momentum space with explicit transversality enforced at every time slice is also given. As an example the geometrical optics limit is discussed and the ray equation is recovered together with the Rytov rotation of the polarization vector.

A broadband squeezed vacuum photon field is characterized by a complex squeezing function. We show that by controlling the wavelength dependence of its phase it is possible to change the dynamics of the atomic polarization interacting with the squeezed vacuum. Such a phase modulation effectively produces a finite range temporal interaction kernel between the two quadratures of the atomic polarization yielding the change in the decay rates as well as the appearance of additional oscillation frequencies. We show that decay rates slower than the spontaneous decay rate can be achieved even for a squeezed bath in the classical regime. For "piecewise linear" and quadratic phase modulations the power spectrum of the scattered light exhibits narrowing of the central peak due to the modified decay rates. For strong phase modulations, side lobes appear symmetrically around the central peak reflecting additional oscillation frequencies.

We consider a semiconductor quantum-well placed in a waveguide microcavity and interacting with the broadband squeezed vacuum radiation, which fills one mode of the waveguide with a large average occupation. The waveguide modifies the optical density of states so that the quantum well interacts mostly with the squeezed vacuum. The vacuum is squeezed around the externally controlled central frequency ω0, which is tuned above the electron-hole gap Eg, and induces fluctuations in the interband polarization of the quantum well. The power spectrum of scattered light exhibits a peak around ω0, which is moreover non-Lorentzian and is a result of both the squeezing and the particle-hole continuum. The squeezing spectrum is qualitatively different from the atomic case. We discuss the possibility of observing the above phenomena in the presence of additional nonradiative (e-e, phonon) dephasing.

In controlled dephasing a controlled environment causes dephasing of transport through a mesoscopic system. As a result of their interaction the states of the two subsystems are entangled. In this paper we discuss how their entanglement influences dephasing using as an example the “which path detector,” where the dephasing of transport through a quantum dot (QD) due to the interaction with a quantum point contact (QPC) is detected by means of an Aharonov-Bohm (AB) interferometer. In particular, we calculate the suppression ν of AB oscillations as a function of the bias eV applied to the QPC and the coupling Γ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from ν ∝ (eV/Γ)², when e V ≪ Γ to ν ∝ eV/Γ, for e V ≫ Γ.

We study the statistics of quasiparticle and quasihole levels in small interacting disordered systems within the Hartree-Fock approximation. The distribution of the inverse compressibility, given according to Koopmans’ theorem by the distance between the two levels across the Fermi energy, evolves from a Wigner distribution in the noninteracting limit to a shifted Gaussian for strong interactions. On the other hand, the nature of the distribution of spacings between neighboring levels on the same side of the Fermi energy (corresponding to energy differences between excited states of the system with one missing or one extra electron) is not affected by the interaction and follows Wigner-Dyson statistics. These results are derived analytically by isolating and solving the appropriate Hartree-Fock equations for the two levels. They are substantiated by numerical simulations of the full set of Hartree-Fock equations for a disordered quantum dot with Coulomb interactions. We find enhanced fluctuations of the inverse compressibility compared to the prediction of the random matrix theory, possibly due to the localization of the wave functions around the edge of the dot. The distribution of the inverse compressibility calculated from the discrete second derivative with respect to the number of particles of the Hartree-Fock ground state energy deviates from the distribution of the level spacing across the Fermi energy. The two distributions have similar shapes but are shifted with respect to each other. The deviation increases with the strength of the interaction thus indicating the breakdown of Koopmans’ theorem in the strongly interacting limit.

Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed mathematical techniques in combination with a standard variational principle to formulate a new variational approach for matrix models. Approximate variational solutions of interacting large-N matrix models are found using the free random matrices as the variational space. Several classes of classical and quantum mechanical matrix models with different types of interactions are considered and the variational solutions compared with exact Monte Carlo and analytical results. Impressive agreement is found in a majority of cases.

The “body fixed frame” with respect to local gauge transformations is introduced. Rigid gauge “rotations” in QCD and their Schrödinger equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the “body fixed” frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroiscopic-like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit.

Quantum tunneling of vortices in very clean type-II superconductors is shown to be governed by the Hall term in the equation of motion. An effective action determining the tunneling probability is calculated. It is argued that high-temperature superconductors may belong to a class of very clean materials, and that they may have Hall tunneling at low temperatures.

A unified framework of the Landau theory of phase transitions in statistical systems is applied to the description of the shape transitions in hot rotating nuclei. Assuming the temperature dependence of the coefficients of the Landau expansion is consistent with the underlying microscopic theory we derive and discuss the most general features of these transitions which are expected to have a universal character. For nuclei with prolate ground states we find rapid changes of the equilibrium shape from almost prolate to oblate when the excitation energy E^* increases in the vicinity of a certain critical value and for a fixed angular momentum J. The rate of these shape transitions depends strongly on the magnitude of J and is faster for smaller J. In the terminology of statistical mechanics the transition is first order when J is less than a certain critical J_c and second order for J > J_c. On the phase diagram of E^* versus J the lines of the first and second order transitions meet at an analog of a tricritical point where large fluctuations around the equilibrium shape are expected. The general theory is illustrated by calculations of the properties and the phase diagram of the ¹⁶⁶Er nucleus.

The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic hamiltonian onto an exactly solvable geometrical hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low-lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operators in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM.

A semi-classical theory based on the path integral formalism is applied to the description of Coulomb fission. Complex classical trajectories are used to compute the classically forbidden transitions from the target's ground state to fission. In a simple model the energy spectrum and angular distributions of the fragments are calculated for the Coulomb fission in the Xe + U collision. Theoretical predictions are made which may be checked experimentally.

The relationship of structure to function in the recognition of ribonuclease S-peptide by S-protein was studied by several methods. Liquid phase peptide synthesis was employed to generate analogs of S-peptide in which from 1 to 8 residues were deleted from the NH2-terminal end of the S-peptide. Additional derivatives were made by substitutions in the NH2-terminal three amino acids or by modifying the S-peptide analogs by trifluoroacetylation. The analogs were generated in the following way. S-Peptide was cleaved with chymotrypsin. The fragment obtained, RNase(9-20), was purified and lengthened step by step using liquid phase peptide synthesis. A second set of analogs were prepared by cleavage of CF3CO-S-peptide with elastase and the resulting CF3CO-RNase(7-20), similarly lengthened. The various analogs of S-peptide were tested in their capacity to combine with S-protein and regenerate biological activity as measured by Vmax and Kb. This work shows a positive contribution of every one of the first 8 NH2-terminal residues of S-peptide to the molecular recognition of S-protein in the presence of RNA substrate. Substitution of the first 3 residues by alanine or blocking of the free amino groups decreases recognition, indicating that the original primary structure is the most favorable one.

A uniform semi-classical approach based on the classical limit of Feynman's path-integral representation is applied for the case of multiple Coulomb excitation. The resulting excitation probabilities are compared with those obtained from the conventional semi-classical treatment and also with the results of the full quantum mechanical coupled channels treatment.