162 research outputs found
Compressional Mode Softening and Euler Buckling Patterns in Mesoscopic Beams
We describe a sequence of Euler buckling instabilities associated with the transverse modes of a mesoscopic beam subjected to compressional strain. As the strain is increased, successively higher normal mode frequencies are driven to zero; each zero signals an instability in the corresponding normal mode that can be realized if all lower instabilities are suppressed by constraints. When expressed in terms of the critical buckling modes, the potential energy functional takes the form of a multimode Ginzburg–Landau system that describes static equilibria in the presence of symmetry breaking forces. This model is used to analyse the complex equilibrium shapes that have been observed experimentally in strained mesoscopic beams. Theoretically predicted critical strain values agree with the appearances of higher order mode structures as the length-to-width aspect ratio increases. The theory also predicts upper bounds on the individual mode amplitudes that are consistent with the data. Based on insights from the theory, we suggest possible origins of the buckling patterns
Dipole binding in a cosmic string background due to quantum anomalies
We propose quantum dynamics for the dipole moving in cosmic string background
and show that the classical scale symmetry of a particle moving in cosmic
string background is still restored even in the presence of dipole moment of
the particle. However, we show that the classical scale symmetry is broken due
to inequivalent quantization of the the non-relativistic system. The
consequence of this quantum anomaly is the formation of bound state in the
interval \xi\in(-1,1). The inequivalent quantization is characterized by a
1-parameter family of self-adjoint extension parameter \Sigma. We show that
within the interval \xi\in(-1,1), cosmic string with zero radius can bind the
dipole and the dipole does not fall into the singularity.Comment: Accepted for publication in Phys. Rev.
Quantum Effects in the Mechanical Properties of Suspended Nanomechanical Systems
We explore the quantum aspects of an elastic bar supported at both ends and
subject to compression. If strain rather than stress is held fixed, the system
remains stable beyond the buckling instability, supporting two potential
minima. The classical equilibrium transverse displacement is analogous to a
Ginsburg-Landau order parameter, with strain playing the role of temperature.
We calculate the quantum fluctuations about the classical value as a function
of strain. Excitation energies and quantum fluctuation amplitudes are compared
for silicon beams and carbon nanotubes.Comment: RevTeX4. 5 pages, 3 eps figures. Submitted to Physical Review Letter
Algebraic treatment of the confluent Natanzon potentials
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas,
the Green's function for the class of the confluent Natanzon potentials is
constructed straightforwardly. The bound-state energy spectrum is then
determined. Eventually, the three-dimensional harmonic potential, the
three-dimensional Coulomb potential and the Morse potential may all be
considered as particular cases.Comment: 9 page
Landau Levels in the noncommutative
We formulate the Landau problem in the context of the noncommutative analog
of a surface of constant negative curvature, that is surface, and
obtain the spectrum and contrast the same with the Landau levels one finds in
the case of the commutative space.Comment: 19 pages, Latex, references and clarifications added including 2
figure
Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions
We present a general derivation of semi-fermionic representation for spin
operators in terms of a bilinear combination of fermions in real and imaginary
time formalisms. The constraint on fermionic occupation numbers is fulfilled by
means of imaginary Lagrange multipliers resulting in special shape of
quasiparticle distribution functions. We show how Schwinger-Keldysh technique
for spin operators is constructed with the help of semi-fermions. We
demonstrate how the idea of semi-fermionic representation might be extended to
the groups possessing dynamic symmetries (e.g. singlet/triplet transitions in
quantum dots). We illustrate the application of semi-fermionic representations
for various problems of strongly correlated and mesoscopic physics.Comment: Review article, 40 pages, 11 figure
Symmetries of the near horizon of a Black Hole by Group Theoretic methods
We use group theoretic methods to obtain the extended Lie point symmetries of
the quantum dynamics of a scalar particle probing the near horizon structure of
a black hole. Symmetries of the classical equations of motion for a charged
particle in the field of an inverse square potential and a monopole, in the
presence of certain model magnetic fields and potentials are also studied. Our
analysis gives the generators and Lie algebras generating the inherent
symmetries.Comment: To appear in Int. J. Mod. Phys.
Random matrix ensemble with random two-body interactions in presence of a mean-field for spin one boson systems
For number of bosons, carrying spin (=1) degree of freedom, in
number of single particle orbitals, each triply degenerate, we
introduce and analyze embedded Gaussian orthogonal ensemble of random matrices
generated by random two-body interactions that are spin (S) scalar
[BEGOE(2)-]. The embedding algebra is with SO(3) generating spin . A method for constructing the ensembles
in fixed-(, ) space has been developed. Numerical calculations show that
the form of the fixed-(, ) density of states is close to Gaussian and
level fluctuations follow GOE. Propagation formulas for the fixed-(, )
space energy centroids and spectral variances are derived for a general one
plus two-body Hamiltonian preserving spin. In addition to these, we also
introduce two different pairing symmetry algebras in the space defined by
BEGOE(2)- and the structure of ground states is studied for each paring
symmetry.Comment: 22 pages, 6 figure
On the use of the group SO(4,2) in atomic and molecular physics
In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like
atom is derived through two different approaches. The first one is by an
established traditional ascent process starting from the symmetry group SO(3).
This approach is presented in a mathematically oriented original way with a
special emphasis on maximally superintegrable systems, N-dimensional extension
and little groups. The second approach is by a new symmetry descent process
starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional
harmonic oscillator. It is based on the little known concept of a Lie algebra
under constraints and corresponds in some sense to a symmetry breaking
mechanism. This paper ends with a brief discussion of the interest of SO(4,2)
for a new group-theoretical approach to the periodic table of chemical
elements. In this connection, a general ongoing programme based on the use of a
complete set of commuting operators is briefly described. It is believed that
the present paper could be useful not only to the atomic and molecular
community but also to people working in theoretical and mathematical physics.Comment: 31 page
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