Victor Mukherjee

Quenching dynamics of a quantumXYspin-12chain in a transverse field

We study the quantum dynamics of a one-dimensional spin-1/2 anisotropic XY model in a transverse field when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. The two quenching schemes are called transverse and anisotropic quenching respectively. Our emphasis in this paper is on the anisotropic quenching scheme and we compare the results with those of the other scheme. In the process of anisotropic quenching, the system crosses all the quantum critical lines of the phase diagram where the relaxation time diverges. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as

Defect production due to quenching through a multicritical point

1/\sqrt{\tau}

Experimental study of space-charge-limited flows in a nanogap

, where

Effects of interference in the dynamics of a spin- 1/2 transverse XY chain driven periodically through quantum critical points

\tau

Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

is the characteristic time scale of quenching, a scenario that supports the Kibble-Zurek mechanism. Interestingly, in the case of anisotropic quenching, there exists an additional non-adiabatic transition, in comparison to the transverse quenching case, with the corresponding probability peaking at an incommensurate value of the wave vector. In the special case in which the system passes through a multi-critical point, the defect density is found to vary as

Defect generation in a spin-\frac{1}{2}\ transverse XY chain under repeated quenching of the transverse field

1/\tau^{1/6}

Loschmidt echo with a nonequilibrium initial state: Early-time scaling and enhanced decoherence

. The von Neumann entropy of the final state is shown to maximize at a quenching rate around which the ordering of the final state changes from antiferromagnetic to ferromagnetic.

Oscillating fidelity susceptibility near a quantum multicritical point

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as t/tau, where tau is the characteristic timescale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects (n) in the final state is not necessarily given by the Kibble-Zurek scaling form n similar to 1/tau(d nu)/((z nu+1)), where d is the spatial dimension, and. and z are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by n similar to 1/(tau d/(2z2)), where the exponent z(2) determines the behavior of the off-diagonal term of the 2 x 2 Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.

Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment

An experimental investigation of space-charge-limited flow of current in a nanogap is presented. Electrodes with gap size d∼70–110nm corresponding to d∕λ0∼(1−5)×103, where λ0 is the de Broglie wavelength of the space-charge electrons are experimented. Unlike classical Child–Langmuir’s (CL) law, the current density varies as square root of applied voltage (V1∕2), when d becomes comparable to λ0. Additionally, a transition regime has been found for the 90nm gap size where the CL law appears at voltages >45V. At d=110nm, the system is found to exhibit purely classical behavior.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the effects of interference on the quenching dynamics of a one-dimensional spin 1/2 XY model in the presence of a transverse field (h(t)) which varies sinusoidally with time as h = h0cos?t, with |t|?tf = ?/?. We have explicitly shown that the finite values of tf make the dynamics inherently dependent on the phases of probability amplitudes, which had been hitherto unseen in all cases of linear quenching with large initial and final times. In contrast, we also consider the situation where the magnetic field consists of an oscillatory as well as a linearly varying component, i.e., h(t) = h0cos?t+t/?, where the interference effects lose importance in the limit of large ?. Our purpose is to estimate the defect density and the local entropy density in the final state if the system is initially prepared in its ground state. For a single crossing through the quantum critical point with h = h0cos?t, the density of defects in the final state is calculated by mapping the dynamics to an equivalent Landau?Zener problem by linearizing near the crossing point, and is found to vary as in the limit of small ?. On the other hand, the local entropy density is found to attain a maximum as a function of ? near a characteristic scale ?0. Extending to the situation of multiple crossings, we show that the role of finite initial and final times of quenching are manifested non-trivially in the interference effects of certain resonance modes which solely contribute to the production of defects. Kink density as well as the diagonal entropy density show oscillatory dependence on the number of full cycles of oscillation. Finally, the inclusion of a linear term in the transverse field on top of the oscillatory component results in a kink density which decreases continuously with ? while it increases monotonically with ?. The entropy density also shows monotonic change with the parameters, increasing with ? and decreasing with ?, in sharp contrast to the situations studied earlier. We also propose appropriate scaling relations for the defect density in the above situations and compare the results with the numerical results obtained by integrating the Schr?dinger equations.