1,588 research outputs found
An Equation of State for Anisotropic Solids under Shock Loading
An anisotropic equation of state is proposed for accurate extrapolation of
high-pressure shock Hugoniot states to other thermodynamics states for shocked
single crystals and polycrystalline alloys. The proposed equation of state
represents mathematical and physical generalization of the Mie-Gr\"{u}neisen
equation of state for isotropic material and reduces to this equation in the
limit of isotropy. Using an anisotropic nonlinear continuum framework and
generalized decomposition of a stress tensor [Int. J. Plasticity \textbf{24},
140 (2008)], the shock waves propagation along arbitrary directions in
anisotropic solids of any symmetry can be examined. The non-associated strength
model includes the distortion effect of the yield surface which can be used to
describe the anisotropic strength differential effect. A numerical calculation
showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and
Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental
data. The results are presented and discussed, and future studies are outlined.Comment: 6 pages, 2 figure
Friedel oscillations of Density of States in a one-dimensional Mott insulator and Incommensurate Charge Density Wave/Superconductor
Oscillations of local density of states generated by a single scalar impurity
potential are calculated for one-dimensional systems with dynamically generated
charge or spin gap. At zero temperature the oscillations develop at finite wave
vector ( for the Mott insulator and for ICDW/SC) and at frequencies
larger than the soliton spectral gap . Their amplitude has a broad maximum
at , where is the gap magnitude.Comment: 4 pages, 2 figure
Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
Relation between the vacuum eigenvalues of CFT Q-operators and spectral
determinants of one-dimensional Schroedinger operator with homogeneous
potential, recently conjectured by Dorey and Tateo for special value of
Virasoro vacuum parameter p, is proven to hold, with suitable modification of
the Schroedinger operator, for all values of p.Comment: 9 pages, harvmac.tex, typos correcte
Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
This paper is a direct continuation of\ \BLZ\ where we begun the study of the
integrable structures in Conformal Field Theory. We show here how to construct
the operators which act in highest weight Virasoro
module and commute for different values of the parameter . These
operators appear to be the CFT analogs of the - matrix of Baxter\ \Baxn, in
particular they satisfy famous Baxter's equation. We also
show that under natural assumptions about analytic properties of the operators
as the functions of the Baxter's relation allows
one to derive the nonlinear integral equations of Destri-de Vega (DDV)\ \dVega\
for the eigenvalues of the -operators. We then use the DDV equation to
obtain the asymptotic expansions of the - operators at large
; it is remarkable that unlike the expansions of the
operators of \ \BLZ, the asymptotic series for contains the
``dual'' nonlocal Integrals of Motion along with the local ones. We also
discuss an intriguing relation between the vacuum eigenvalues of the
- operators and the stationary transport properties in boundary sine-Gordon
model. On this basis we propose a number of new exact results about finite
voltage charge transport through the point contact in quantum Hall system.Comment: Revised version, 43 pages, harvmac.tex. Minor changes, references
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Wave function renormalization constants and one-particle form factors in Toda field theories
We apply the method of angular quantization to calculation of the wave
function renormali- zation constants in affine Toda quantum field
theories. A general formula for the wave function renormalization constants in
ADE Toda field theories is proposed. We also calculate all one-particle form
factors and some of the two-particle form factors of an exponential field.Comment: harvmac, 28 pages, 2 eps figures, misprints correcte
Bukhvostov-Lipatov model and quantum-classical duality
The Bukhvostov-Lipatov model is an exactly soluble model of two interacting
Dirac fermions in 1+1 dimensions. The model describes weakly interacting
instantons and anti-instantons in the non-linear sigma model. In our
previous work [arXiv:1607.04839] we have proposed an exact formula for the
vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of
the classical sinh-Gordon equation, which can be viewed as an example of a
remarkable duality between integrable quantum field theories and integrable
classical field theories in two dimensions. Here we present a complete
derivation of this duality based on the classical inverse scattering transform
method, traditional Bethe ansatz techniques and analytic theory of ordinary
differential equations. In particular, we show that the Bethe ansatz equations
defining the vacuum state of the quantum theory also define connection
coefficients of an auxiliary linear problem for the classical sinh-Gordon
equation. Moreover, we also present details of the derivation of the non-linear
integral equations determining the vacuum energy and other spectral
characteristics of the model in the case when the vacuum state is filled by
2-string solutions of the Bethe ansatz equations.Comment: 49 pages, 8 figure
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