Ara Sedrakyan
Yerevan State University, Theoretical Physics, Faculty Member
- I am Professor of physics at Yerevan Physics Institute.edit
In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points... more
In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface S and its dual S^* made of quadrangular and n-gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Klümper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.
We construct an effective low energy Hamiltonian which describes fermions dwelling on a deformed honeycomb lattice with dislocations and disclinations, and with an arbitrary hopping parameters of the corresponding tight binding model. It... more
We construct an effective low energy Hamiltonian which describes fermions dwelling on a deformed honeycomb lattice with dislocations and disclinations, and with an arbitrary hopping parameters of the corresponding tight binding model. It describes the interaction of fermions with a 2d gravity and has also a local SU(2) gauge invariance of the group of rotations. We reformulate the model as interaction of fermions with the deformation of the lattice, which forms a phonon field. We calculate the response of fermion currents to the external deformation or phonon field, which is a result of a Z_2 anomaly. This can be detected experimentally.
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We construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of... more
We construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang-Baxter equations. This construction yields P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry.
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The Lagrangian (action) formulation of the Chalker-Coddington network model for plateau-plateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice ($ML$). The dimensionless Landauer... more
The Lagrangian (action) formulation of the Chalker-Coddington network model for plateau-plateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice ($ML$). The dimensionless Landauer resistance is considered and its average is calculated over the random U(1) phases with constant distribution on the circle. The Lagrangian of the resultant model on $ML$ is found and the corresponding $R$-matrix is written down. It appeared, that this model is integrable, rising hope to investigate physics of plateau- plateau transitions by the exact method of powerful Algebraic Bethe Ansatz $(ABA)$.
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We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag... more
We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.
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The technique of construction on Manhattan lattice (ML) the fermionic action for Integrable models is presented. The Sign-Factor of 3D Ising model (SF of 3DIM) and Chalker-Coddington-s phenomenological model (CCM) for the edge excitations... more
The technique of construction on Manhattan lattice (ML) the fermionic action for Integrable models is presented. The Sign-Factor of 3D Ising model (SF of 3DIM) and Chalker-Coddington-s phenomenological model (CCM) for the edge excitations in Hall effect are formulated in this way. The second one demonstrates the necessity to consider the inhomogeneous models with staggered R-matrices. The disorder over the U(1) phases is taken into account and staggered Hubbard type of model is obtained. The technique is developed to construct the integrable models with staggered disposition of R-matrices.
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The technique of construction on Manhattan lattice (ML) the fermionic action for Integrable models is presented. The Sign-Factor of 3D Ising model (SF of 3DIM) and Chalker-Coddington-s phenomenological model (CCM) for the edge excitations... more
The technique of construction on Manhattan lattice (ML) the fermionic action for Integrable models is presented. The Sign-Factor of 3D Ising model (SF of 3DIM) and Chalker-Coddington-s phenomenological model (CCM) for the edge excitations in Hall effect are formulated in this way. The second one demonstrates the necessity to consider the inhomogeneous models with staggered R-matrices. The disorder over the U(1) phases is taken into account and staggered Hubbard type of model is obtained. The technique is developed to construct the integrable models with staggered disposition of R-matrices.
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In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points... more
In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface S and its dual S∗ made of quadrangular and n−gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Klümper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.
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Protein molecules can be approximated by discrete polygonal chains of amino acids. Standard topological tools can be applied to the smoothening of the polygons to introduce a topological classification of folded states of proteins, for... more
Protein molecules can be approximated by discrete polygonal chains of amino acids. Standard topological tools can be applied to the smoothening of the polygons to introduce a topological classification of folded states of proteins, for example, using the self-linking number of the corresponding framed curves. In this paper we extend this classification to the discrete version, taking advantage of the “randomness” of such curves. Known definitions of the self-linking number apply to non-singular framings: for example, the Frenet framing cannot be used if the curve has inflection points. However, in the discrete proteins the special points are naturally resolved. Consequently, a separate integer topological characteristics can be introduced, which takes into account the intrinsic features of the special points. This works well for the proteins in our analysis, for which we compute integer topological indices associated with the singularities of the Frenet framing. We show how a versio...
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The Frenet equation governs the extrinsic geometry of a string in three-dimensional ambient space in terms of the curvature and torsion, which are both scalar functions under string reparameterisations. The description engages a local... more
The Frenet equation governs the extrinsic geometry of a string in three-dimensional ambient space in terms of the curvature and torsion, which are both scalar functions under string reparameterisations. The description engages a local SO(2) gauge symmetry, which emerges from the invariance of the extrinsic string geometry under local frame rotations around the tangent vector. Here we inquire how to construct the most general SO(2) gauge invariant Hamiltonian of strings, in terms of the curvature and torsion. The construction instructs us to introduce a long-range (self-) interaction between strings, which is mediated by a three dimensional bulk gauge field with a Chern-Simons self-interaction. The results support the proposal that fractional statistics should be prevalent in the case of three dimensional string-like configurations.
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We analyze the t-dependence of the trajectories of many-particle Regge poles. These poles realize the idea of Mandelstam (Comm. on Nuclear and Particle Physics. 3, 3 (1969), and elsewhere) concerning the role of t-channel many-particle... more
We analyze the t-dependence of the trajectories of many-particle Regge poles. These poles realize the idea of Mandelstam (Comm. on Nuclear and Particle Physics. 3, 3 (1969), and elsewhere) concerning the role of t-channel many-particle states in the formation of growing Rege trajectories.
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We have calculated the leading logarithmic asymptote of the generalized ladders of phi³ theory in which each ladder interacts with any other via a maximum number of exchanges. It is shown that this asymptote is determined by Regge poles... more
We have calculated the leading logarithmic asymptote of the generalized ladders of phi³ theory in which each ladder interacts with any other via a maximum number of exchanges. It is shown that this asymptote is determined by Regge poles arising from the t-channel multiparticle states, and that the intercept increases quadratically as the number of particles in this channel increases. We consider the possibility that the Pomeron is an assembly of a large number of interconnected ladders.
It is shown that in the phi³ theory there exist Regge poles made up of many-particle states in the t channel. Their intercept increases quadratically with the number of particles in this channel. (AIP)
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The quantum-mechanical problem of a multiparticle bound state with maximum angular momentum that depends quadratically on the number of particles is studied from the point of view of the multiparticle reggeon considered previously by the... more
The quantum-mechanical problem of a multiparticle bound state with maximum angular momentum that depends quadratically on the number of particles is studied from the point of view of the multiparticle reggeon considered previously by the authors (S.G. Matinyan and A.G. Sedrakyan, Pis'ma Zh. Eksp. Teor. Fiz. 23, 588 (1976) (JETP Lett. 23, 538 (1976)); Yad. Fiz. 24, 844 (1976) (Sov. J. Nucl. Phys. 24, 440 (1976))). The conditions under which the intercept of such a reggeon is greater than unity are discussed.
The intercept and slope of the trajectory of a multi-particle Regge pole are determined as a function of the number of particles in the t-channel, with allowance for the ''repulsion'' between particles of neighboring... more
The intercept and slope of the trajectory of a multi-particle Regge pole are determined as a function of the number of particles in the t-channel, with allowance for the ''repulsion'' between particles of neighboring rapidities in the ladder configurations. If this ''repulsion'' is taken into account, the quadratic dependence of the intercept on N is replaced by a weaker dependence (approx.N ln N) in the case of 2N particles in the t-channel with Ng²>1.
The determinant of induced Dirac action for fermions living on a two-dimensional surface immersed with Whitney singularities into 3D Euclidean space is calculated exactly in Weyl invariant regularization.
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The universal R-matrices on Verma modules of U q sl 2 and U q sl ^ 2 are considered in the case that q denotes a root of unity. There is a renormalization procedure to exclude the singularities of the R-matrix, which usually take place in... more
The universal R-matrices on Verma modules of U q sl 2 and U q sl ^ 2 are considered in the case that q denotes a root of unity. There is a renormalization procedure to exclude the singularities of the R-matrix, which usually take place in the root of unity case. A connection with the autoquasitriangular Hopf algebras defined by N. Reshetikhin [cf. Commun. Math. Phys. 170, 79-99 (1995; Zbl 0838.17009)] is pointed out.
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We numerically calculated the localization length index ν and up to two subleading finite-size indices in the Chalker-Coddington network model of the plateau-plateau transitions in the quantum Hall effect. We also carried out fits with... more
We numerically calculated the localization length index ν and up to two subleading finite-size indices in the Chalker-Coddington network model of the plateau-plateau transitions in the quantum Hall effect. We also carried out fits with logarithmic corrections. The confidence intervals of the four fits for the exponent ν are narrow and overlap. The fit based on one relevant field and one marginal field is slightly more advantageous in comparison to the fits based on a relevant field and irrelevant field. The calculations were carried out by two different programs that produced close results, each one within the error bars of the other.
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We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral... more
We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.
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ABSTRACT We construct integrable models with a ℤ 2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter Equations are written... more
ABSTRACT We construct integrable models with a ℤ 2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter Equations are written down and their solution for the gl(N) case are found. The symmetry behind these models can be interpreted as the tensor product of the (-1)-Weyl algebra by an extension U q (gl(N)) with a Cartan generator related to deformation parameter -1. We analyze in detail the case N=2. It can be regarded as quantum U qℬ (gl(2)) group with a matrix deformation parameter qℬ with (qℬ) 2 =q 2 .