289 research outputs found
Gauge-potential approach to the kinematics of a moving car
A kinematics of the motion of a car is reformulated in terms of the theory of
gauge potentials (connection on principal bundle). E(2)-connection originates
in the no-slipping contact of the car with a road.Comment: 13 pages, AmsTe
Loschmidt echo and stochastic-like quantum dynamics of nano-particles
We investigate time evolution of prepared vibrational state (system) coupled
to a reservoir with dense spectrum of its vibrational states. We assume that
the reservoir has an equidistant spectrum, and the system - reservoir coupling
matrix elements are independent of the reservoir states. The analytical
solution manifests three regimes of the evolution for the system: (I) weakly
damped oscillations; (II) multicomponent Loschmidt echo in recurrence cycles;
(III) overlapping recurrence cycles. We find the characteristic critical values
of the system - reservoir coupling constant for the transitions between these
regimes. Stochastic dynamics occurs in the regime (III) due to inevoidably in
any real system coarse graining of time or energy measurements, or initial
condition uncertainty. Even though a specific toy model is investigated here,
when properly interpreted it yields quite reasonable description for a variety
of physically relevant phenomena.Comment: 8 pages, 3 figure
On Conformal Infinity and Compactifications of the Minkowski Space
Using the standard Cayley transform and elementary tools it is reiterated
that the conformal compactification of the Minkowski space involves not only
the "cone at infinity" but also the 2-sphere that is at the base of this cone.
We represent this 2-sphere by two additionally marked points on the Penrose
diagram for the compactified Minkowski space. Lacks and omissions in the
existing literature are described, Penrose diagrams are derived for both,
simple compactification and its double covering space, which is discussed in
some detail using both the U(2) approach and the exterior and Clifford algebra
methods. Using the Hodge * operator twistors (i.e. vectors of the
pseudo-Hermitian space H_{2,2}) are realized as spinors (i.e., vectors of a
faithful irreducible representation of the even Clifford algebra) for the
conformal group SO(4,2)/Z_2. Killing vector fields corresponding to the left
action of U(2) on itself are explicitly calculated. Isotropic cones and
corresponding projective quadrics in H_{p,q} are also discussed. Applications
to flat conformal structures, including the normal Cartan connection and
conformal development has been discussed in some detail.Comment: 38 pages, 8 figures, late
Rigorous Formulation of Duality in Gravitational Theories
In this paper we evince a rigorous formulation of duality in gravitational
theories where an Einstein like equation is valid, by providing the conditions
under which the Hodge duals (with respect to the metric tensor g) of T^a and
R_b^a may be considered as the torsion and curvature 2-forms associated with a
connection D', part of a Riemann-Cartan structure (M,g',D'), in the cases g =
g' and g does not equal g', once T^a and R_b^a are the torsion and curvature
2-forms associated with a connection D part of a Riemann-Cartan structure
(M,g,D). A new form for the Einstein equation involving the dual of the Riemann
tensor of D is also provided, and the result is compared with others appearing
in the literature.Comment: 15 page
Plane waves in a relativistic homogeneous and isotropic elastic continuum
Propagation of gravitational and acoustic plane waves in a flat universe
filled with a general relativistic, homogeneous and isotropic, spatially flat
continuum is studied. The continuum is described by analogues of
nonrelativistic characteristics, namely energy per particle, pressure and Lame
coefficients, and considered in the comoving proper-time gauge. For all modes
with the given wave covector, differential equations governing the time
dependence of the amplitudes are derived. In particular, longitudinal acoustic
waves are described, in analogy with the nonrelativistic theory, by two coupled
first-order equations. As an example, plane waves in a stiff ultrarigid
continuum are considered.Comment: 12 pages, 1 figure; section 4 extended, minor changes elsewhere,
author adde
Dynamic and spectral mixing in nanosystems
In the framework of simple spin-boson Hamiltonian we study an interplay
between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian
describes an initial vibrational state coupled to discrete dense spectrum
reservoir. The reservoir states are formed by three sequences with rationally
independent periodicities typical for vibrational states in many nanosize
systems. We show that quantum evolution of the system is determined by a
dimensionless parameter which is characteristic number of the reservoir states
relevant for the initial vibrational level dynamics. Our semi-quantitative
analytic results are confirmed by numerical solution of the equation of motion.
We anticipate that predicted in the paper both kinds of stochastic-like
behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing)
can be observed by femtosecond spectroscopy methods in nanosystems.Comment: 6 pages, 4 figure
Two-Dimensional Spectroscopy of Extended Molecular Systems: Applications to Energy Transport and Relaxation in an α-Helix
A simulation study of the coupled dynamics of amide I and amide II vibrations in an α-helix dissolved in water shows that two-dimensional (2D) infrared spectroscopy may be used to disentangle the energy transport along the helix through each of these modes from the energy relaxation between them. Time scales for both types of processes are obtained. Using polarization-dependent 2D spectroscopy is an important ingredient in the method we propose. The method may also be applied to other two-band systems, both in the infrared (collective vibrations) and the visible (excitons) parts of the spectrum.
Terahertz underdamped vibrational motion governs protein-ligand binding in solution
Low-frequency collective vibrational modes in proteins have been proposed as being responsible for efficiently directing biochemical reactions and biological energy transport. However, evidence of the existence of delocalized vibrational modes is scarce and proof of their involvement in biological function absent. Here we apply extremely sensitive femtosecond optical Kerr-effect spectroscopy to study the depolarized Raman spectra of lysozyme and its complex with the inhibitor triacetylchitotriose in solution. Underdamped delocalized vibrational modes in the terahertz frequency domain are identified and shown to blue-shift and strengthen upon inhibitor binding. This demonstrates that the ligand-binding coordinate in proteins is underdamped and not simply solvent-controlled as previously assumed. The presence of such underdamped delocalized modes in proteins may have significant implications for the understanding of the efficiency of ligand binding and protein–molecule interactions, and has wider implications for biochemical reactivity and biological function
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