89,207 research outputs found
Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force
In classical mechanics, a nonrelativistic particle constrained on an
curved hypersurface embedded in flat space experiences the centripetal
force only. In quantum mechanics, the situation is totally different for the
presence of the geometric potential. We demonstrate that the motion of the
quantum particle is "driven" by not only the the centripetal force, but also a
curvature induced force proportional to the Laplacian of the mean curvature,
which is fundamental in the interface physics, causing curvature driven
interface evolution.Comment: 4 page
The centripetal force law and the equation of motion for a particle on a curved hypersurface
It is pointed out that the current form of extrinsic equation of motion for a
particle constrained to remain on a hypersurface is in fact a half-finished
version for it is established without regard to the fact that the particle can
never depart from the geodesics on the surface. Once the fact be taken into
consideration, the equation takes that same form as that for centripetal force
law, provided that the symbols are re-interpreted so that the law is applicable
for higher dimensions. The controversial issue of constructing operator forms
of these equations is addressed, and our studies show the quantization of
constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio
Sound radiation in turbulent channel flows
Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit
Efficient solutions of self-consistent mean field equations for dewetting and electrostatics in nonuniform liquids
We use a new configuration-based version of linear response theory to
efficiently solve self-consistent mean field equations relating an effective
single particle potential to the induced density. The versatility and accuracy
of the method is illustrated by applications to dewetting of a hard sphere
solute in a Lennard-Jones fluid, the interplay between local hydrogen bond
structure and electrostatics for water confined between two hydrophobic walls,
and to ion pairing in ionic solutions. Simulation time has been reduced by more
than an order of magnitude over previous methods.Comment: Supplementary material included at end of main pape
Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice
We investigate a Bose-Einstein condensate trapped in a 2D optical lattice in
the presence of weak disorder within the framework of the Bogoliubov theory. In
particular, we analyze the combined effects of disorder and an optical lattice
on quantum fluctuations and superfluid density of the BEC system. Accordingly,
the analytical expressions of the ground state energy and quantum depletion of
the system are obtained. Our results show that the lattice still induces a
characteristic 3D to 1D crossover in the behavior of quantum fluctuations,
despite the presence of weak disorder. Furthermore, we use the linear response
theory to calculate the normal fluid density of the condensate induced by
disorder. Our results in the 3D regime show that the combined presence of
disorder and lattice induce a normal fluid density that asymptotically
approaches 4/3 of the corresponding condensate depletion. Conditions for
possible experimental realization of our scenario are also proposed.Comment: 8 pages, 0 figure. To appear in Physical Review
Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalized zeta functions
For quantum fields on a curved spacetime with an Euclidean section, we derive
a general expression for the stress energy tensor two-point function in terms
of the effective action. The renormalized two-point function is given in terms
of the second variation of the Mellin transform of the trace of the heat kernel
for the quantum fields. For systems for which a spectral decomposition of the
wave opearator is possible, we give an exact expression for this two-point
function. Explicit examples of the variance to the mean ratio of the vacuum energy density of a
massless scalar field are computed for the spatial topologies of and , with results of , and
respectively. The large variance signifies the importance
of quantum fluctuations and has important implications for the validity of
semiclassical gravity theories at sub-Planckian scales. The method presented
here can facilitate the calculation of stress-energy fluctuations for quantum
fields useful for the analysis of fluctuation effects and critical phenomena in
problems ranging from atom optics and mesoscopic physics to early universe and
black hole physics.Comment: Uses revte
Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
A method is given to compute an approximation to the noise kernel, defined as
the symmetrized connected 2-point function of the stress tensor, for the
conformally invariant scalar field in any spacetime conformal to an
ultra-static spacetime for the case in which the field is in a thermal state at
an arbitrary temperature. The most useful applications of the method are flat
space where the approximation is exact and Schwarzschild spacetime where the
approximation is better than it is in most other spacetimes. The two points are
assumed to be separated in a timelike or spacelike direction. The method
involves the use of a Gaussian approximation which is of the same type as that
used by Page to compute an approximate form of the stress tensor for this field
in Schwarzschild spacetime. All components of the noise kernel have been
computed exactly for hot flat space and one component is explicitly displayed.
Several components have also been computed for Schwarzschild spacetime and
again one component is explicitly displayed.Comment: 34 pages, no figures. Substantial revisions in Secs. I, IV, and V;
minor revisions elsewhere; new results include computation of the exact noise
kernel for hot flat space and an approximate computation of the noise kernel
for a thermal state at an arbitrary temperature in Schwarzschild spacetime
when the points are split in the time directio
Entanglement creation between two causally-disconnected objects
We study the full entanglement dynamics of two uniformly accelerated
Unruh-DeWitt detectors with no direct interaction in between but each coupled
to a common quantum field and moving back-to-back in the field vacuum. For two
detectors initially prepared in a separable state our exact results show that
quantum entanglement between the detectors can be created by the quantum field
under some specific circumstances, though each detector never enters the
other's light cone in this setup. In the weak coupling limit, this entanglement
creation can occur only if the initial moment is placed early enough and the
proper acceleration of the detectors is not too large or too small compared to
the natural frequency of the detectors. Once entanglement is created it lasts
only a finite duration, and always disappears at late times. Prior result by
Reznik derived using the time-dependent perturbation theory with extended
integration domain is shown to be a limiting case of our exact solutions at
some specific moment. In the strong coupling and high acceleration regime,
vacuum fluctuations experienced by each detector locally always dominate over
the cross correlations between the detectors, so entanglement between the
detectors will never be generated.Comment: 16 pages, 8 figures; added Ref.[7] and related discussion
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