arXiv subjects

Sergei Khlebnikov

Publications and source records attributed to Sergei Khlebnikov.

28 records · Page 2Linked to original sources

arXiv2013

Re-gauging groupoid, symmetries and degeneracies for Graph Hamiltonians and applications to the Gyroid wire network

We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)--commutative geometries. By selecting gauging data these geometries are realized by matrices through an explicit construction or a Kan-extension. We describe the changes in gauge via the action of a regauging groupoid. It acts via matrices that give rise to a noncommutative 2--cocycle and hence to a groupoid extension (gerbe). We furthermore show that automorphisms of the underlying graph of the quiver can be lifted to extended symmetry groups of regaugings. In the commutative case, we deduce that the extended symmetries act via a projective representation. This yields isotypical decompositions and super--selection rules. We apply these results to the PDG and honeycomb wire--networks using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the G(yroid) and the honeycomb systems.

math-ph↗

arXiv2013

Winding branes and persistent currents

A D5 brane winding around a stack of D3 branes can be used as a model of persistent current in a thin superconducting ring, with the number N of D3s corresponding to the number of transverse channels in the ring. We consider, in the large N limit, existence and properties of a gapped superconducting state with a uniform winding number density q. We find that there is a gapped classical solution for any q, no matter how large, but when q is larger than a certain q_m the state is unstable with respect to decay by phase slips. We argue that this decay produces strings via a version of the Hanany-Witten effect (in a non-transverse, non-supersymmetric arrangement of branes). This parallels the requirement of quasiparticle production in a clean (disorder-free) wire in field theory of superconductivity.

hep-th↗

arXiv2013

Critical current of a superconducting wire via gauge/gravity duality

We describe application of the gauge/gravity duality to study of thin superconducting wires at finite current. The large number N of colors of the gauge theory is identified with the number of filled transverse channels in the wire. On the gravity side, the physics is described by a system of D3 and D5 branes intersecting over a line. We consider the ground state of the system at fixed electric current and find that at zero temperature the normal state is always unstable with respect to appearance of a superconducting component. We discuss relation of our results to recent experiments on statistics of the switching current in nanowires.

hep-th↗

arXiv2013

Geometry of the momentum space: From wire networks to quivers and monopoles

A new nano--material in the form of a double gyroid has motivated us to study (non-commutative $C^*$ geometry of periodic wire networks and the associated graph Hamiltonians. Here we present the general abstract framework, which is given by certain quiver representations, with special attention to the original case of the gyroid as well as related cases, such as graphene. In these geometric situations, the non- commutativity is introduced by a constant magnetic field and the theory splits into two pieces: commutative and non-commutative, both of which are governed by a $C^*$ geometry. In the non-commutative case, we can use tools such as K-theory to make statements about the band structure. In the commutative case, we give geometric and algebraic methods to study band intersections; these methods come from singularity theory and representation theory. We also provide new tools in the study, using $K$-theory and Chern classes. The latter can be computed using Berry connection in the momentum space. This brings monopole charges and issues of topological stability into the picture.

math-ph↗

arXiv2012

The geometry of the Double Gyroid wire network: Quantum and Classical

Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.

math-ph↗

arXiv2012

The noncommutative geometry of wire networks from triply periodic surfaces

We study wire networks that are the complements of triply periodic minimal surfaces. Here we consider the P, D, G surfaces which are exactly the cases in which the corresponding graphs are symmetric and self-dual. Our approach is using the Harper Hamiltonian in a constant magnetic field. We treat this system with the methods of noncommutative geometry and obtain a classification for all the $C^*$ geometries that appear.

math-ph↗

arXiv2012

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of $A_n$ type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an $A_k$ singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.

math-ph↗

arXiv2011

Shock waves in strongly coupled plasmas II

In a recent paper we have analyzed the AdS/CFT duals to shock waves propagating in the N=4 plasma. Here we study further properties of the system. In the gravity description we consider the properties of the dual black holes, showing in particular that they are stationary black holes with expanding horizons. This is possible because the horizon is not compact; in the fluid, this corresponds to the situation when entropy is being produced and carried away to infinity. We also consider shocks in dimensionalities d other than four and find that, for plasmas whose duals are given by asymptotically AdS spaces, the exponential tail of the shock on the supersonic side shrinks as gamma^(-2/d) as the velocity approaches the speed of light (the Lorentz factor gamma goes to infinity). This generalizes the behavior gamma^(-1/2) we have found previously for d=4. Finally, we consider corrugations of the shock front and show that the shock is stable under such perturbations. There are, however, long lived modes, excitations of which describe generation of sound by the shock wave, the energy for this being provided by the incoming fluid.

hep-th↗

arXiv2010

Shock waves in strongly coupled plasmas

Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically $AdS_5$ space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks we find the dual metric in a derivative expansion and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular we find that, when the velocity of the fluid relative to the shock approaches the speed of light $v\to 1$ the penetration depth $\ell$ scales as $\ell\sim (1-v^2)^{1/4}$. We compare the results with second order hydrodynamics and the Israel-Stewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.

hep-th↗

arXiv2010

Effect of strain on stripe phases in the Quantum Hall regime

Spontaneous breaking of rotational symmetry and preferential orientation of stripe phases in the quantum Hall regime has attracted considerable experimental and theoretical effort over the last decade. We demonstrate experimentally and theoretically that the direction of high and low resistance of the two-dimensional (2D) hole gas in the quantum Hall regime can be controlled by an external strain. Depending on the sign of the in-plane shear strain, the Hartree-Fock energy of holes or electrons is minimized when the charge density wave (CDW) is oriented along [110] or [1-10] directions. We suggest that shear strains due to internal electric fields in the growth direction are responsible for the observed orientation of CDW in pristine electron and hole samples.

cond-mat.str-el↗