1,041 research outputs found
Nambu-Jona-Lasinio Model Coupled to Constant Electromagnetic Fields in D-Dimension
Critical dynamics of the Nambu-Jona-Lasinio model, coupled to a constant
electromagnetic field in D=2, 3, and 4, is reconsidered from a viewpoint of
infrared behavior and vacuum instability. The latter is associated with
constant electric fields and cannot be avoidable in the nonperturbative
framework obtained through the proper time method. As for magnetic fields, an
infrared cut-off is essential to investigate the critical phenomena. The result
reconfirms the fact that the critical coupling in D=3 and 4 goes to zero even
under an infinitesimal magnetic field. There also shows that a non-vanishing
causes instability. A perturbation with
respect to external fields is adopted to investigate critical quantities, but
the resultant asymptotic expansion excellently matches with the exact value.Comment: 27 pages, 17 figure files, LaTe
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
Plankton sampling from the Aurora Australis and the Shirase in 2009–2013 —NORPAC standard net & closing net samples—
Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?
Probably not.Comment: 10 pages, 1 figur
Reduction of quantum systems on Riemannian manifolds with symmetry and application to molecular mechanics
This paper deals with a general method for the reduction of quantum systems
with symmetry. For a Riemannian manifold M admitting a compact Lie group G as
an isometry group, the quotient space Q = M/G is not a smooth manifold in
general but stratified into a collection of smooth manifolds of various
dimensions. If the action of the compact group G is free, M is made into a
principal fiber bundle with structure group G. In this case, reduced quantum
systems are set up as quantum systems on the associated vector bundles over Q =
M/G. This idea of reduction fails, if the action of G on M is not free.
However, the Peter-Weyl theorem works well for reducing quantum systems on M.
When applied to the space of wave functions on M, the Peter-Weyl theorem
provides the decomposition of the space of wave functions into spaces of
equivariant functions on M, which are interpreted as Hilbert spaces for reduced
quantum systems on Q. The concept of connection on a principal fiber bundle is
generalized to be defined well on the stratified manifold M. Then the reduced
Laplacian is well defined as a self-adjoint operator with the boundary
conditions on singular sets of lower dimensions. Application to quantum
molecular mechanics is also discussed in detail. In fact, the reduction of
quantum systems studied in this paper stems from molecular mechanics. If one
wishes to consider the molecule which is allowed to lie in a line when it is in
motion, the reduction method presented in this paper works well.Comment: 33 pages, no figure
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
One-center small polarons as short-lived precursors in self-trapping processes of holes and electron-hole pairs in alkali iodides
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