arXiv subjects

Aavishkar A. Patel

Publications and source records attributed to Aavishkar A. Patel.

43 records · Page 3Linked to original sources

arXiv2013

Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Loschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.

cond-mat.mes-hall↗

arXiv2013

Role of marginality in quantum fidelity and Loschmidt echo: Dirac points in 2-D

We investigate the effect of marginality on the ground state fidelity and Loschmidt echo. For this purpose, we study the above quantities near the quantum critical point (QCP) of the two-dimensional (2-D) Dirac Hamiltonian in the presence of a mass term which is tuned to zero at the Dirac point. An ideal example would be that of the low-energy carriers in graphene in which a mass term opens up a band gap. This happens to be a marginal situation where the behavior of the fidelity and the echo is markedly different as compared to that in the one-dimensional case. We encounter this marginal behavior near the Dirac point, which is displayed in the absence of a sharp dip in the ground state fidelity (or equivalently in the logarithmic scaling of the fidelity susceptibility). Most importantly, there is also a logarithmic correction to the proposed scaling of the fidelity in the thermodynamic limit which can not be a priori anticipated from the predicted scaling form. Interestingly, a sharp dip in the ground state Loschmidt echo is also found to be absent near this QCP, which is again a consequence of the marginality. We also explain the absence of a sharp dip in both the fidelity and the Loschmidt echo close to the QCP in dimensions greater than two.

cond-mat.mes-hall↗

arXiv2012

Sudden quenching in the Kitaev honeycomb model: Study of defect and heat generation

We study the behavior of the defect and heat densities under sudden quenching near the quantum critical points in the two-dimensional Kitaev honeycomb model both in the thermodynamic and non-thermodynamic limits. We consider quenches starting from a quantum critical point into the gapped as well as the gapless phases. We choose points on the lines of anisotropic quantum critical points as well as different points of intersection of these lines as the initial points from where the quenching starts. We find that the defect and heat densities display the expected power-law scalings along with logarithmic corrections to scaling (or cusp singularities) in certain cases. In the vicinity of some of the intersection points the scaling behaviors change, indicating an effective dimensional reduction; the scaling behavior near these points depends on the number of critical lines crossed in the process of quenching. All the analytical predictions are also verified by numerical integration.

cond-mat.stat-mech↗

arXiv2012

Classical and quantum magneto-oscillations of current flow near a p-n junction in graphene

The proposed semiclassical theory predicts two types of oscillations in the flow of current injected from a point source near a ballistic p-n junction in graphene in a strong magnetic field. One originates from the classical effect of bunching of cyclotron orbits of electrons passing back and forth across the p-n interface, which displays a pronounced dependence on the commensurability between the cyclotron radii in the n- and p-regions. The other effect is caused by the interference of monochromatic electron waves in p-n junctions with equal carrier densities on the two sides and it consists in magneto-oscillations in the current transmission through the interface with periodicity similar to Shubnikov-de Haas oscillations.

cond-mat.mes-hall↗

arXiv2011

Skipping and snake orbits of electrons: singularities and catastrophes

Near the sample edge, or a sharp magnetic field step the drift of two-dimensional electrons in a magnetic field has the form of skipping/snake orbits. We show that families of skipping/snake orbits of electrons injected at one point inside a 2D metal generically exhibit caustics folds, cusps and cusp triplets, and, in one extreme case, a section of the batterfly bifurcation. Periodic appearance of singularities along the $\pm B$-interface leads to the magneto-oscillations of nonlocal conductance in multi-terminal electronic devices.

cond-mat.mes-hall↗

arXiv2010

Theromelectricity in Graphene: Effects of a gap and magnetic fields

We calculate the thermopower of monolayer graphene in various circumstances. First we show that experiments on the thermopower of graphene can be understood quantitatively with a very simple model of screening in the semiclassical limit. We can calculate the energy dependent scattering time for this model exactly. We then consider acoustic phonon scattering which might be the operative scattering mechanism in free standing films, and predict that the thermopower will be linear in any induced gap in the system. Further, the thermopower peaks at the same value of chemical potential (tunable by gate voltage) independent of the gap. Finally, we show that in the semiclassical approximation, the thermopower in a magnetic field saturates at high field to a value which can be calculated exactly and is independent of the details of the scattering. This effect might be observable experimentally.

cond-mat.mtrl-sci↗

arXiv2007

A Coupled Oscillator Model for Grover's Quantum Database Search Algorithm

Grover's database search algorithm is the optimal algorithm for finding a desired object from an unsorted collection of items. Although it was discovered in the context of quantum computation, it is simple and versatile enough to be implemented using any physical system that allows superposition of states, and several proposals have been made in the literature. I study a mechanical realisation of the algorithm using coupled simple harmonic oscillators, and construct its physical model for the simplest case of four identical oscillators. The identification oracle is implemented as an elastic reflection of the desired oscillator, and the overrelaxation operation is realised as evolution of the system by half an oscillation period. I derive the equations of motion, and solve them both analytically and by computer simulation. I extend the ideal case analysis and explore the sensitivity of the algorithm to changes in the initial conditions, masses of springs and damping. The amplitude amplification provided by the algorithm enhances the energy of the desired oscillator, while running the algorithm backwards spreads out the energy of the perturbed oscillator among its partners. The former (efficient focusing of energy into a specific oscillator) can have interesting applications in processes that need crossing of an energy threshold for completion, and can be useful in nanotechnological devices and catalysis. The latter (efficient redistribution of energy) can be useful in processes requiring rapid dissipation of energy, such as shock-absorbers and vibrational shielding. I present some tentative proposals.

physics.gen-ph↗