DSpace Academic/Research Unit: Pure & Applied Mathematics
http://hdl.handle.net/2262/59
Pure & Applied Mathematics2014-02-26T11:34:18ZObituary: T. Trevor West 1938-2012
http://hdl.handle.net/2262/68138
Title: Obituary: T. Trevor West 1938-2012
Author: TIMONEY, RICHARD
Description: PUBLISHED2014-02-25T00:00:00ZThe Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
http://hdl.handle.net/2262/67631
Title: The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
Author: Constantin, Adrian; Lannes, David
Abstract: n recent years two nonlinear dispersive partial differential equations have attracted much attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a flat bed. The equations capture stronger nonlinear effects than the classical nonlinear dispersive Benjamin–Bona–Mahoney and Korteweg–de Vries equations. In particular, they accommodate wave breaking phenomena.2009-03-31T23:00:00ZSupercritical biharmonic equations with power-type nonlinearity
http://hdl.handle.net/2262/67618
Title: Supercritical biharmonic equations with power-type nonlinearity
Author: KARAGEORGIS, PASCHALIS
Abstract: We study two different versions of a supercritical biharmonic equation with a power-type nonlinearity. First, we focus on the equation Delta(2)u = vertical bar u vertical bar(p-1)u over the whole space R(n), where n > 4 and p > (n + 4)/(n - 4). Assuming that p < p(c), where p(c) is a further critical exponent, we show that all regular radial solutions oscillate around an explicit singular radial solution. As it was already known, on the other hand, no such oscillations occur in the remaining case p >= p(c). We also study the Dirichlet problem for the equation Delta(2)u = lambda(1 + u)(p) over the unit ball in R(n), where lambda > 0 is an eigenvalue parameter, while n > 4 and p > (n + 4)/(n - 4) as before. When it comes to the extremal solution associated to this eigenvalue problem, we show that it is regular as long as p < p(c). Finally, we show that a singular solution exists for some appropriate lambda > 0
Description: PUBLISHED2009-01-01T00:00:00ZStatic Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
http://hdl.handle.net/2262/67560
Title: Static Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
Author: FROLOV, SERGEY
Abstract: Motivated by the notorious di culties in determining the rst quantum corrections
to the spectrum of short strings in
AdS
5
S
5
from rst principles, we study closed
bosonic strings in this background employing a static gauge. In this gauge the
world-sheet Hamiltonian density is constant along the extension of the string and
directly proportional to the square of the spacetime energy. We quantize this sys-
tem in a minisuperspace approach, in which we consider only a single
AdS
5
string
mode excitation next to an arbitrary particle like zero-mode contribution in the full
AdS
5
S
5
background. We determine the quantum spectrum using this method to
the next-to-next-to-leading order in the large 't Hooft coupling expansion. We ar-
gue for an ordering prescription which should arise from supersymmetrization and
indeed recover the integrability based predictions for the spectrum of the lightest
excitation, dual to the Konishi eld scaling dimensions. The higher excitations
fail to agree, but this is shown to be a consequence of the string mode truncation
employed. Despite this simple setup, our system reveals intriguing features, such
as a close connection to particles in
AdS 6 , classical integrability and preservation
of the isometries of
AdS 5 S 5 at the quantum level
Description: PUBLISHED2013-01-01T00:00:00ZFree field representation and form factors of the chiral Gross-Neveu model
http://hdl.handle.net/2262/67559
Title: Free field representation and form factors of the chiral Gross-Neveu model
Author: BRITTON, STEPHEN K; FROLOV, SERGEY
Abstract: The free field representation of the Zamolodchikov-Faddeev algebra for
the chiral Gross-Neveu model is analysed in detail, and used to construct an integral
representation for form factors of the model
Description: PUBLISHED2013-01-01T00:00:00ZExcited states in Bethe ansatz solvable models and the dressing of spin and charge
http://hdl.handle.net/2262/67558
Title: Excited states in Bethe ansatz solvable models and the dressing of spin and charge
Author: FROLOV, SERGEY
Abstract: A general formalism for the study of excitations above equilibrium in Bethe ansatz
solvable models is presented. Nonzero temperature expressions for dressed energy,
momentum, spin and charge are obtained. The zero temperature excitations of the
Hubbard-Shastry models are examined in detail, and special attention is paid to the
dressing of spin and charge of excited quasi-particles. These are in general momentum
dependent and are only spin-charge separated when the ground state is half- lled and
has zero magnetisation
Description: PUBLISHED2013-01-01T00:00:00ZExceptional Operators in N=4 super Yang-Mills
http://hdl.handle.net/2262/66905
Title: Exceptional Operators in N=4 super Yang-Mills
Author: FROLOV, SERGEY
Abstract: We consider one particularly interesting class of composite gauge-invariant op-
erators in
N
= 4 super Yang-Mills theory. An exceptional feature of these operators is that
in the Thermodynamic Bethe Ansatz approach the one-loop rapidities of the constituent
magnons are shown to be exact in the 't Hooft coupling constant. This is used to propose
the mirror TBA description for these operators. The proposal is shown to pass several
non-trivial checks.
Description: PUBLISHED2012-01-01T00:00:00ZScaling dimensions from the mirror TBA
http://hdl.handle.net/2262/66904
Title: Scaling dimensions from the mirror TBA
Author: FROLOV, SERGEY
Abstract: The mirror TBA equations proposed by Arutyunov, Suzuki and the author are solved numerically up to 't Hooft's coupling $\lambda\approx 2340$ for several two-particle states dual to ${\cal N}=4$ SYM operators from the $\sl(2)$ sector. The data obtained for states with mode numbers $n=1,2,3,4$ is used to propose a general charge $J$ dependent formula for the first nonvanishing subleading coefficient in the strong coupling expansion of scaling dimensions. In addition we find that the first critical and subcritical values of the coupling for the $J=4, n=1$ operator are at $\lambda\approx 133$ and $\lambda\approx 190$, respectively.
Description: PUBLISHED2012-01-01T00:00:00ZHubbard Shastry lattice models
http://hdl.handle.net/2262/66903
Title: Hubbard Shastry lattice models
Author: FROLOV, SERGEY
Abstract: We consider two lattice models for strongly correlated electrons which are exactly solvable in one dimension. Along with the Hubbard model and the $\mathfrak {su}(2|2)$ spin chain, these are the only parity-invariant models that can be obtained from Shastry's R-matrix. One exhibits itinerant ferromagnetic behaviour, while for the other the electrons form bound pairs and at half-filling the model becomes insulating. We derive the thermodynamic Bethe ansatz equations for the models, analyse them at various limits, and in particular obtain zero temperature phase diagrams. Furthermore, we consider extensions of the models, which reduce to the Essler–Korepin–Schoutens model in certain limits.
Description: PUBLISHED2012-01-01T00:00:00ZBound states in the mirror TBA
http://hdl.handle.net/2262/66902
Title: Bound states in the mirror TBA
Author: FROLOV, SERGEY
Abstract: The spectrum of the light-cone AdS
5
S
5
superstring contains states composed
of particles with complex momenta including in particular those which turn into bound
states in the decompacti cation limit. We propose the mirror TBA description for these
states. We focus on a three-particle state which is a nite-size representative of a scattering
state of a fundamental particle and a two-particle bound state and dual to an operator from
the
su
(2) sector of
N
= 4 SYM. We nd that the analytic behavior of Y-functions di ers
drastically from the case of states with real momenta. Most importantly,
Y
Q
-functions
exhibit poles in the analyticity strip which leads to the appearance of new terms in the
formula for the energy of this state. In addition, the TBA equations are supplied by
quantization conditions which involve
Y
2
. Considering yet another example of a three-
particle state, we nd that the corresponding quantization conditions do not even involve
Y
1
. Our treatment can be generalized to a wide class of states with complex momenta
Description: PUBLISHED2012-01-01T00:00:00Z