1,122 research outputs found
Quantization on a torus without position operators
We formulate quantum mechanics in the two-dimensional torus without using
position operators. We define an algebra with only momentum operators and shift
operators and construct irreducible representation of the algebra. We show that
it realizes quantum mechanics of a charged particle in a uniform magnetic
field. We prove that any irreducible representation of the algebra is unitary
equivalent to each other. This work provides a firm foundation for the
noncommutative torus theory.Comment: 12 pages, LaTeX2e, the title is changed, minor corrections are made,
references are added. To be published in Modern Physics Letters
Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two- dimensionalcorrelation spectroscopy
We theoretically investigate an electron transfer (ET) process in a
dissipative environment by means of two-dimensional (2D) correlation
spectroscopy. We extend the reduced hierarchy equations of motion approach to
include both overdamped Drude and underdamped Brownian modes. While the
overdamped mode describes the inhomogeneity of a system in the slow modulation
limit, the underdamped mode expresses the primary vibrational mode coupled with
the electronic states. We outline a procedure for calculating 2D correlation
spectrum that incorporates the ET processes. The present approach has the
capability of dealing with system-bath coherence under an external
perturbation, which is important to calculate nonlinear response functions for
non-Markovian noise. The calculated 2D spectrum exhibits the effects of the ET
processes through the presence of ET transition peaks along the
axis, as well as the decay of echo signals.Comment: 28 pages, 8 figures; J. Chem. Phys. 137 (2012
Dirac monopole with Feynman brackets
We introduce the magnetic angular momentum as a consequence of the structure
of the sO(3) Lie algebra defined by the Feynman brackets. The Poincare momentum
and Dirac magnetic monopole appears as a direct result of this framework.Comment: 10 page
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
Correlated fluctuations in the exciton dynamics and spectroscopy of DNA
The absorption of ultraviolet light creates excitations in DNA, which
subsequently start moving in the helix. Their fate is important for an
understanding of photo damage, and is determined by the interplay of electronic
couplings between bases and the structure of the DNA environment. We model the
effect of dynamical fluctuations in the environment and study correlation,
which is present when multiple base pairs interact with the same mode in the
environment. We find that the correlations strongly affect the exciton
dynamics, and show how they are observed in the decay of the anisotropy as a
function of a coherence and a population time in a non-linear optical
experiment
An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian
We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic
field in the n-dimensional torus. We obtained a complete set of solutions for a
broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a
quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice
{\Lambda}. The lattice is not necessary either cubic or rectangular. The
magnetic field is also arbitrary. However, we restrict ourselves within
potential-free problems; the Schr{\"o}dinger operator is assumed to be the
Laplace operator defined with the covariant derivative. We defined an algebra
that characterizes the symmetry of the Laplacian and named it the magnetic
algebra. We proved that the space of functions on which the Laplacian acts is
an irreducible representation space of the magnetic algebra. In this sense the
magnetic algebra completely characterizes the quantum mechanics in the magnetic
torus. We developed a new method for Fourier analysis for the magnetic torus
and used it to solve the eigenvalue problem of the Laplacian. All the
eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad
Optical signatures of intrinsic electron localization in amorphous SiO2
We measure and analyse the optical absorption spectra of three silica glass samples irradiated with 1 MeV electrons at 80 K, where self-trapped holes are stable, and use ab initio calculations to demonstrate that these spectra contain a signature of intrinsic electron traps created as counterparts to the holes. In particular, we argue that optical absorption bands peaking at 3.7, 4.7, and 6.4âeV belong to strongly localised electrons trapped at precursor sites in amorphous structure characterized by strained SiâO bonds and OâSiâO angles greater than 132°. These results are important for our understanding of the properties of silica glass and other silicates as well as the reliability of electronic and optical devices and for luminescence dating
Epitaxial checkerboard arrangement of nanorods in ZnMnGaO4 films studied by x-ray diffraction
The intriguing nano-structural properties of a ZnMnGaO4 film epitaxially
grown on MgO (001) substrate have been investigated using synchrotron
radiation-based x-ray diffraction. The ZnMnGaO4 film consisted of a
self-assembled checkerboard (CB) structure with perfectly aligned and regularly
spaced vertical nanorods. The lattice parameters of the orthorhombic and
rotated tetragonal phases of the CB structure were analyzed using H-K, H-L, and
K-L cross sections of the reciprocal space maps measured around various
symmetric and asymmetric reflections of the spinel structure. We demonstrate
that the symmetry of atomic displacements at the phases boundaries provides the
means for coherent coexistence of two domains types within the volume of the
film
Some boundary effects in quantum field theory
We have constructed a quantum field theory in a finite box, with periodic
boundary conditions, using the hypothesis that particles living in a finite box
are created and/or annihilated by the creation and/or annihilation operators,
respectively, of a quantum harmonic oscillator on a circle. An expression for
the effective coupling constant is obtained showing explicitly its dependence
on the dimension of the box.Comment: 12 pages, Late
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
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