Hierarchical Equations of Motion Approach to Quantum Thermodynamics

We present a theoretical framework to investigate quantum thermodynamic processes under non-Markovian system-bath interactions on the basis of the hierarchical equations of motion (HEOM) approach, which is convenient to carry out numerically "exact" calculations. This formalism is valuable because it can be used to treat not only strong system-bath coupling but also system-bath correlation or entanglement, which will be essential to characterize the heat transport between the system and quantum heat baths. Using this formalism, we demonstrated an importance of the thermodynamic effect from the tri-partite correlations (TPC) for a two-level heat transfer model and a three-level autonomous heat engine model under the conditions that the conventional quantum master equation approaches are failed. Our numerical calculations show that TPC contributions, which distinguish the heat current from the energy current, have to be take into account to satisfy the thermodynamic laws.Comment: 9 pages, 4 figures. As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT

Direct observation of the proliferation of ferroelectric loop domains and vortex-antivortex pairs

We discovered "stripe" patterns of trimerization-ferroelectric domains in hexagonal REMnO3 (RE=Ho, ---, Lu) crystals (grown below ferroelectric transition temperatures (Tc), reaching up to 1435 oC), in contrast with the vortex patterns in YMnO3. These stripe patterns roughen with the appearance of numerous loop domains through thermal annealing just below Tc, but the stripe domain patterns turn to vortex-antivortex domain patterns through a freezing process when crystals cross Tc even though the phase transition appears not to be Kosterlitz-Thouless-type. The experimental systematics are compared with the results of our six-state clock model simulation and also the Kibble-Zurek Mechanism for trapped topological defects

An evaporation-based model of thermal neutron induced ternary fission of plutonium

Ternary fission probabilities for thermal neutron induced fission of plutonium are analyzed within the framework of an evaporation-based model where the complexity of time-varying potentials, associated with the neck collapse, are included in a simplistic fashion. If the nuclear temperature at scission and the fission-neck-collapse time are assumed to be ~1.2 MeV and ~10^-22 s, respectively, then calculated relative probabilities of ternary-fission light-charged-particle emission follow the trends seen in the experimental data. The ability of this model to reproduce ternary fission probabilities spanning seven orders of magnitude for a wide range of light-particle charges and masses implies that ternary fission is caused by the coupling of an evaporation-like process with the rapid re-arrangement of the nuclear fluid following scission.Comment: 25 pages, 12 figures, accepted for publication in IJMP

Coupled-channels analysis of the 16^{{\bf 16}}O+208^{{\bf 208}}Pb fusion barrier distribution

Analyses using simplified coupled-channels models have been unable to describe the shape of the previously measured fusion barrier distribution for the doubly magic $^{16}$O+$^{208}$Pb system. This problem was investigated by re-measuring the fission excitation function for $^{16}$O+$^{208}$Pb with improved accuracy and performing more exact coupled-channels calculations, avoiding the constant-coupling and first-order coupling approximations often used in simplified analyses. Couplings to the single- and 2-phonon states of $^{208}$Pb, correctly taking into account the excitation energy and the phonon character of these states, particle transfers, and the effects of varying the diffuseness of the nuclear potential, were all explored. However, in contrast to other recent analyses of precise fusion data, no satisfactory simultaneous description of the shape of the experimental barrier distribution and the fusion cross-sections for $^{16}$O+$^{208}$Pb was obtained.Comment: RevTex, 29 pages, 7 postscript figures, to appear in PR

First-principles calculations of the self-trapped exciton in crystalline NaCl

The atomic and electronic structure of the lowest triplet state of the off-center (C2v symmetry) self-trapped exciton (STE) in crystalline NaCl is calculated using the local-spin-density (LSDA) approximation. In addition, the Franck-Condon broadening of the luminescence peak and the a1g -> b3u absorption peak are calculated and compared to experiment. LSDA accurately predicts transition energies if the initial and final states are both localized or delocalized, but 1 eV discrepancies with experiment occur if one state is localized and the other is delocalized.Comment: 4 pages with 4 embeddded figure

Modelling charge self-trapping in wide-gap dielectrics: Localization problem in local density functionals

We discuss the adiabatic self-trapping of small polarons within the density functional theory (DFT). In particular, we carried out plane-wave pseudo-potential calculations of the triplet exciton in NaCl and found no energy minimum corresponding to the self-trapped exciton (STE) contrary to the experimental evidence and previous calculations. To explore the origin of this problem we modelled the self-trapped hole in NaCl using hybrid density functionals and an embedded cluster method. Calculations show that the stability of the self-trapped state of the hole drastically depends on the amount of the exact exchange in the density functional: at less than 30% of the Hartree-Fock exchange, only delocalized hole is stable, at 50% - both delocalized and self-trapped states are stable, while further increase of exact exchange results in only the self-trapped state being stable. We argue that the main contributions to the self-trapping energy such as the kinetic energy of the localizing charge, the chemical bond formation of the di-halogen quasi molecule, and the lattice polarization, are represented incorrectly within the Kohn-Sham (KS) based approaches.Comment: 6 figures, 1 tabl