In fast forward quantum shortcuts to adiabaticity, a designed potential UF F (q, t) steers a wave... more In fast forward quantum shortcuts to adiabaticity, a designed potential UF F (q, t) steers a wavefunction to evolve from the n'th eigenstate of an initial HamiltonianĤ(0) to the n'th eigenstate of a final HamiltonianĤ(τ), in finite time τ. Previously proposed strategies for constructing UF F are (in the absence of special symmetries) limited to the ground state, n = 0. We develop a method that overcomes this limitation, thereby substantially expanding the applicability of this shortcut to adiabaticity, and we illustrate its effectiveness with numerical simulations. Semiclassical analysis provides insight and establishes a close correspondence with the analogous classical fast forward method.
Journal of Statistical Mechanics: Theory and Experiment, Mar 28, 2011
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in... more We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle η. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points 'quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter α that defines a path, upto a critical value α = αc = 2. For α > αc, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.
International Journal of Modern Physics B, Nov 26, 2012
We review recent studies on the measures of zero temperature quantum correlations namely, the qua... more We review recent studies on the measures of zero temperature quantum correlations namely, the quantum entanglement (concurrence) and discord present in the final state of a transverse XY spin chain following a quench through quantum critical points; the aim of these studies is to explore the scaling of the above quantities as a function of the quench rate. A comparative study between the concurrence and the quantum discord shows that their behavior is qualitatively the same though there are quantitative differences. For the present model, the scaling of both the quantities are given by the scaling of the density of the defect present in the final state though one can not find a closed form expression for the discord. We also extend our study of quantum discord to a transverse Ising chain in the presence of a three spin interaction. Finally, we present a study of the dynamical evolution of quantum discord and concurrence when two central qubits, initially prepared in a Werner state, are coupled to the environmental XY spin chain which is driven through quantum critical points. The qualitative behavior of quantum discord and concurrence are found to be similar as that of the decoherence factor.
Landauer's Principle states that the energy cost of information processing must exceed the produc... more Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature, Boltzmann's constant, and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations-that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allow for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as the square of the information-storing system's length scale. As a paradigmatic example, we design shortcuts to create, erase, and transfer a bit of information metastably stored in a double-well potential. Though dissipated work generally increases with operation fidelity, we show that it is possible to compute with perfect fidelity in finite time with finite work. We also show that the robustness of information storage affects an operation's ener-Communicated by Sebastian Deffner.
Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabatici... more Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum HamiltonianĤCD is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian HCD ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions or translations of the system. Here we investigate an example of a non-scale-invariant system-a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian HCD(q, p, t), which we then quantize to obtain a Hermitian operator HCD(t). Using numerical simulations, we find thatĤCD effectively suppresses non-adiabatic excitations under rapid driving. These results offer a proof of principle-beyond the special case of scale-invariant driving-that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.
Title of dissertation: BRIDGING QUANTUM, CLASSICAL AND STOCHASTIC SHORTCUTS TO ADIABATICITY. Ayot... more Title of dissertation: BRIDGING QUANTUM, CLASSICAL AND STOCHASTIC SHORTCUTS TO ADIABATICITY. Ayoti Patra, Doctor of Philosophy, 2017 Dissertation directed by: Professor Christopher Jarzynski Department of Chemistry and Biochemistry; Institute for Physical Science and Technology; Department of Physics. Adiabatic invariants – quantities that are preserved under the slow driving of a system’s external parameters – are important in classical mechanics, quantum mechanics and thermodynamics. Adiabatic processes allow a system to be guided to evolve to a desired final state. However, the slow driving of a quantum system makes it vulnerable to environmental decoherence, and for both quantum and classical systems, it is often desirable and time-efficient to speed up a process. Shortcuts to adiabaticity are strategies for preserving adiabatic invariants under rapid driving, typically by means of an auxiliary field that suppresses excitations, otherwise generated during rapid driving. Several ...
Author(s): Boyd, AB; Patra, A; Jarzynski, C; Crutchfield, JP | Abstract: Landauer's Principle... more Author(s): Boyd, AB; Patra, A; Jarzynski, C; Crutchfield, JP | Abstract: Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations -- that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allows for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as t...
In fast-forward quantum shortcuts to adiabaticity, a designed potential U FF (q, t) steers a wave... more In fast-forward quantum shortcuts to adiabaticity, a designed potential U FF (q, t) steers a wave function to evolve from the nth eigenstate of an initial HamiltonianĤ (0) to the nth eigenstate of a final HamiltonianĤ (τ), in finite time τ. Previously proposed strategies for constructing U FF are (in the absence of special symmetries) limited to the ground state n = 0. We develop a method that overcomes this limitation, thereby substantially expanding the applicability of this shortcut to adiabaticity, and we illustrate its effectiveness with numerical simulations. Semiclassical analysis provides insight and establishes a close correspondence to the analogous classical fast-forward method.
Shortcuts to adiabaticity assisted by counterdiabatic Born-Oppenheimer dynamics Callum W Duncan a... more Shortcuts to adiabaticity assisted by counterdiabatic Born-Oppenheimer dynamics Callum W Duncan and Adolfo del Campo-Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance Shumpei Masuda et al
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic co... more We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian H = p 2 /2m + U (q, t) in one degree of freedom, and for an arbitrary choice of action I 0 , we construct a "fast-forward" potential energy function V FF (q, t) that, when added to H, guides all trajectories with initial action I 0 to end with the same value of action. We use this result to construct a local dynamical invariant J(q, p, t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final s... more A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe for instance expansion and transport. To this end, we use the formalism of generating functions, and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems.
We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point... more We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point (MCP) using the example of a one-dimensional spin-1/2 transverse XY spin chain. We summarize earlier results of defect generenation and fidelity susceptibility for quenching through MCP and close to the MCP, respectively. For a quenching scheme which enables the system to hit the MCP along different paths, we emphasize the role of path on exponents associated with quasicritical points which appear in the scaling relations. Finally, we explicitly derive the scaling of concurrence and negativity for two spin entanglement generated following a slow quenching across the MCP and enlist the results for different quenching schemes. We explicity show the dependence of the scaling on the quenching path and dicuss the limiting situations.
Journal of Statistical Mechanics: Theory and Experiment, 2011
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in... more We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle φ. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points 'quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter α that defines a path, upto a critical value α = αc = 2. For α > αc, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.
Journal of Statistical Mechanics: Theory and Experiment, 2011
We report a study on the zero-temperature quantum discord as a measure of two-spin correlation of... more We report a study on the zero-temperature quantum discord as a measure of two-spin correlation of a transverse XY spin chain following a quench across a quantum critical point and investigate the behavior of mutual information, classical correlations and hence of discord in the final state as a function of the rate of quenching. We show that though discord vanishes in the limit of very slow as well as very fast quenching, it exhibits a peak for an intermediate value of the quenching rate. We show that though discord and also the mutual information exhibit a similar behavior with respect to the quenching rate to that of concurrence or negativity following an identical quenching, there are quantitative differences. Our studies indicate that like concurrence, discord also exhibits a power law scaling with the rate of quenching in the limit of slow quenching though it may not be expressible in a closed power law form. We also explore the behavior of discord on quenching linearly across a quantum multicritical point (MCP) and observe a scaling similar to that of the defect density.
We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point... more We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point (MCP) using the example of a one-dimensional spin-1/2 transverse XY spin chain. We summarize earlier results of defect generenation and fidelity susceptibility for ...
We review recent studies on the measures of zero temperature quantum correlations namely, the qua... more We review recent studies on the measures of zero temperature quantum correlations namely, the quantum entanglement (concurrence) and discord present in the final state of a transverse XY spin chain following a quench through quantum critical points; the aim of these studies is to explore the scaling of the above quantities as a function of the quench rate. A comparative study between the concurrence and the quantum discord shows that their behavior is qualitatively the same though there are quantitative differences. For the present model, the scaling of both the quantities are given by the scaling of the density of the defect present in the final state though one can not find a closed form expression for the discord. We also extend our study of quantum discord to a transverse Ising chain in the presence of a three spin interaction. Finally, we present a study of the dynamical evolution of quantum discord and concurrence when two central qubits, initially prepared in a Werner state, are coupled to the environmental XY spin chain which is driven through quantum critical points. The qualitative behavior of quantum discord and concurrence are found to be similar as that of the decoherence factor.
In fast forward quantum shortcuts to adiabaticity, a designed potential UF F (q, t) steers a wave... more In fast forward quantum shortcuts to adiabaticity, a designed potential UF F (q, t) steers a wavefunction to evolve from the n'th eigenstate of an initial HamiltonianĤ(0) to the n'th eigenstate of a final HamiltonianĤ(τ), in finite time τ. Previously proposed strategies for constructing UF F are (in the absence of special symmetries) limited to the ground state, n = 0. We develop a method that overcomes this limitation, thereby substantially expanding the applicability of this shortcut to adiabaticity, and we illustrate its effectiveness with numerical simulations. Semiclassical analysis provides insight and establishes a close correspondence with the analogous classical fast forward method.
Journal of Statistical Mechanics: Theory and Experiment, Mar 28, 2011
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in... more We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle η. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points 'quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter α that defines a path, upto a critical value α = αc = 2. For α > αc, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.
International Journal of Modern Physics B, Nov 26, 2012
We review recent studies on the measures of zero temperature quantum correlations namely, the qua... more We review recent studies on the measures of zero temperature quantum correlations namely, the quantum entanglement (concurrence) and discord present in the final state of a transverse XY spin chain following a quench through quantum critical points; the aim of these studies is to explore the scaling of the above quantities as a function of the quench rate. A comparative study between the concurrence and the quantum discord shows that their behavior is qualitatively the same though there are quantitative differences. For the present model, the scaling of both the quantities are given by the scaling of the density of the defect present in the final state though one can not find a closed form expression for the discord. We also extend our study of quantum discord to a transverse Ising chain in the presence of a three spin interaction. Finally, we present a study of the dynamical evolution of quantum discord and concurrence when two central qubits, initially prepared in a Werner state, are coupled to the environmental XY spin chain which is driven through quantum critical points. The qualitative behavior of quantum discord and concurrence are found to be similar as that of the decoherence factor.
Landauer's Principle states that the energy cost of information processing must exceed the produc... more Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature, Boltzmann's constant, and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations-that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allow for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as the square of the information-storing system's length scale. As a paradigmatic example, we design shortcuts to create, erase, and transfer a bit of information metastably stored in a double-well potential. Though dissipated work generally increases with operation fidelity, we show that it is possible to compute with perfect fidelity in finite time with finite work. We also show that the robustness of information storage affects an operation's ener-Communicated by Sebastian Deffner.
Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabatici... more Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum HamiltonianĤCD is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian HCD ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions or translations of the system. Here we investigate an example of a non-scale-invariant system-a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian HCD(q, p, t), which we then quantize to obtain a Hermitian operator HCD(t). Using numerical simulations, we find thatĤCD effectively suppresses non-adiabatic excitations under rapid driving. These results offer a proof of principle-beyond the special case of scale-invariant driving-that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.
Title of dissertation: BRIDGING QUANTUM, CLASSICAL AND STOCHASTIC SHORTCUTS TO ADIABATICITY. Ayot... more Title of dissertation: BRIDGING QUANTUM, CLASSICAL AND STOCHASTIC SHORTCUTS TO ADIABATICITY. Ayoti Patra, Doctor of Philosophy, 2017 Dissertation directed by: Professor Christopher Jarzynski Department of Chemistry and Biochemistry; Institute for Physical Science and Technology; Department of Physics. Adiabatic invariants – quantities that are preserved under the slow driving of a system’s external parameters – are important in classical mechanics, quantum mechanics and thermodynamics. Adiabatic processes allow a system to be guided to evolve to a desired final state. However, the slow driving of a quantum system makes it vulnerable to environmental decoherence, and for both quantum and classical systems, it is often desirable and time-efficient to speed up a process. Shortcuts to adiabaticity are strategies for preserving adiabatic invariants under rapid driving, typically by means of an auxiliary field that suppresses excitations, otherwise generated during rapid driving. Several ...
Author(s): Boyd, AB; Patra, A; Jarzynski, C; Crutchfield, JP | Abstract: Landauer's Principle... more Author(s): Boyd, AB; Patra, A; Jarzynski, C; Crutchfield, JP | Abstract: Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations -- that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allows for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as t...
In fast-forward quantum shortcuts to adiabaticity, a designed potential U FF (q, t) steers a wave... more In fast-forward quantum shortcuts to adiabaticity, a designed potential U FF (q, t) steers a wave function to evolve from the nth eigenstate of an initial HamiltonianĤ (0) to the nth eigenstate of a final HamiltonianĤ (τ), in finite time τ. Previously proposed strategies for constructing U FF are (in the absence of special symmetries) limited to the ground state n = 0. We develop a method that overcomes this limitation, thereby substantially expanding the applicability of this shortcut to adiabaticity, and we illustrate its effectiveness with numerical simulations. Semiclassical analysis provides insight and establishes a close correspondence to the analogous classical fast-forward method.
Shortcuts to adiabaticity assisted by counterdiabatic Born-Oppenheimer dynamics Callum W Duncan a... more Shortcuts to adiabaticity assisted by counterdiabatic Born-Oppenheimer dynamics Callum W Duncan and Adolfo del Campo-Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance Shumpei Masuda et al
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic co... more We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian H = p 2 /2m + U (q, t) in one degree of freedom, and for an arbitrary choice of action I 0 , we construct a "fast-forward" potential energy function V FF (q, t) that, when added to H, guides all trajectories with initial action I 0 to end with the same value of action. We use this result to construct a local dynamical invariant J(q, p, t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final s... more A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe for instance expansion and transport. To this end, we use the formalism of generating functions, and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems.
We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point... more We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point (MCP) using the example of a one-dimensional spin-1/2 transverse XY spin chain. We summarize earlier results of defect generenation and fidelity susceptibility for quenching through MCP and close to the MCP, respectively. For a quenching scheme which enables the system to hit the MCP along different paths, we emphasize the role of path on exponents associated with quasicritical points which appear in the scaling relations. Finally, we explicitly derive the scaling of concurrence and negativity for two spin entanglement generated following a slow quenching across the MCP and enlist the results for different quenching schemes. We explicity show the dependence of the scaling on the quenching path and dicuss the limiting situations.
Journal of Statistical Mechanics: Theory and Experiment, 2011
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in... more We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle φ. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points 'quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter α that defines a path, upto a critical value α = αc = 2. For α > αc, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.
Journal of Statistical Mechanics: Theory and Experiment, 2011
We report a study on the zero-temperature quantum discord as a measure of two-spin correlation of... more We report a study on the zero-temperature quantum discord as a measure of two-spin correlation of a transverse XY spin chain following a quench across a quantum critical point and investigate the behavior of mutual information, classical correlations and hence of discord in the final state as a function of the rate of quenching. We show that though discord vanishes in the limit of very slow as well as very fast quenching, it exhibits a peak for an intermediate value of the quenching rate. We show that though discord and also the mutual information exhibit a similar behavior with respect to the quenching rate to that of concurrence or negativity following an identical quenching, there are quantitative differences. Our studies indicate that like concurrence, discord also exhibits a power law scaling with the rate of quenching in the limit of slow quenching though it may not be expressible in a closed power law form. We also explore the behavior of discord on quenching linearly across a quantum multicritical point (MCP) and observe a scaling similar to that of the defect density.
We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point... more We study the non-equilibrium dynamics of a quantum system close to a quantum multi-critical point (MCP) using the example of a one-dimensional spin-1/2 transverse XY spin chain. We summarize earlier results of defect generenation and fidelity susceptibility for ...
We review recent studies on the measures of zero temperature quantum correlations namely, the qua... more We review recent studies on the measures of zero temperature quantum correlations namely, the quantum entanglement (concurrence) and discord present in the final state of a transverse XY spin chain following a quench through quantum critical points; the aim of these studies is to explore the scaling of the above quantities as a function of the quench rate. A comparative study between the concurrence and the quantum discord shows that their behavior is qualitatively the same though there are quantitative differences. For the present model, the scaling of both the quantities are given by the scaling of the density of the defect present in the final state though one can not find a closed form expression for the discord. We also extend our study of quantum discord to a transverse Ising chain in the presence of a three spin interaction. Finally, we present a study of the dynamical evolution of quantum discord and concurrence when two central qubits, initially prepared in a Werner state, are coupled to the environmental XY spin chain which is driven through quantum critical points. The qualitative behavior of quantum discord and concurrence are found to be similar as that of the decoherence factor.
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Papers by Ayoti Patra