The first and second moments for the quantum Brownian planar rotator in external harmonic classical field

We derive explicit expressions for the first and second moments as well as the correlation function for a planar (one-dimensional) quantum Brownian rotator placed in the external harmonic potential. Our results directly provide the standard deviations for the azimuthal angle and the canonically conjugate angular momentum for the rotator. We find that there are some significant physical differences between this model and the free rotator model, which is well investigated in the literature.

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Vortex states in an acoustic Weyl crystal with a topological lattice defect

Nature Communications ◽

10.1038/s41467-021-23963-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Qiang Wang ◽

Yong Ge ◽

Hong-xiang Sun ◽

Haoran Xue ◽

Ding Jia ◽

...

Keyword(s):

Angular Momentum ◽

Orbital Angular Momentum ◽

Lattice Defect ◽

Three Dimensional ◽

Surface States ◽

Real Space ◽

Lattice Defects ◽

One Dimensional ◽

Topological Features ◽

Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

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The gas-liquid surface of the penetrable sphere model. II

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1978.0009 ◽

1978 ◽

Vol 358 (1694) ◽

pp. 267-280 ◽

Cited By ~ 5

Keyword(s):

Surface Tension ◽

Correlation Function ◽

Liquid Surface ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Intermolecular Potential ◽

Direct Correlation Function ◽

Sphere Model ◽

One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

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Correlation-function asymptotic expansions: Universality of prefactors of the one-dimensional Hubbard model

Physical Review B ◽

10.1103/physrevb.73.113112 ◽

2006 ◽

Vol 73 (11) ◽

Cited By ~ 4

Author(s):

J. M. P. Carmelo ◽

K. Penc

Keyword(s):

Correlation Function ◽

Hubbard Model ◽

Asymptotic Expansions ◽

One Dimensional ◽

The One

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Essentially nonlinear one-dimensional model of classical field theory (Addendum)

Theoretical and Mathematical Physics ◽

10.1007/bf01036500 ◽

1975 ◽

Vol 22 (1) ◽

pp. 100-100 ◽

Cited By ~ 5

Author(s):

L. A. Takhtadzhyan ◽

L. D. Faddeev

Keyword(s):

Field Theory ◽

Classical Field Theory ◽

Classical Field ◽

Dimensional Model ◽

One Dimensional

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The linear potential eigenenergy equation. I: the coefficients Kn(3l′)

Canadian Journal of Physics ◽

10.1139/p79-057 ◽

1979 ◽

Vol 57 (3) ◽

pp. 417-427 ◽

Cited By ~ 6

Author(s):

Adel F. Antippa ◽

Toan Nguyen Ky

Keyword(s):

Angular Momentum ◽

Quantum Number ◽

Asymptotic Limit ◽

Linear Potential ◽

Angular Momentum Quantum Number ◽

Explicit Expressions

We derive explicit expressions for the coefficients Kn(l) of the linear potential eigenenergy equation for values of the angular momentum quantum number given by l = 3l′. The coefficients Kn(3l′) are obtained by taking the asymptotic limit of the previously derived functions Kn3k+1(3l′), as k → ∞.

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