213 research outputs found
The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points
We study the scaling of the decoherence factor of a qubit (spin-1/2) using
the central spin model in which the central spin (qubit) is globally coupled to
a transverse XY spin chain. The aim here is to study the non-equilibrium
generation of decoherence when the spin chain is driven across (along) quantum
critical points (lines) and derive the scaling of the decoherence factor in
terms of the driving rate and some of the exponents associated with the quantum
critical points. Our studies show that the scaling of logarithm of decoherence
factor is identical to that of the defect density in the final state of the
spin chain following a quench across isolated quantum critical points for both
linear and non-linear variations of a parameter even if the defect density may
not satisfy the standard Kibble-Zurek scaling. However, one finds an
interesting deviation when the spin chain is driven along a critical line. Our
analytical predictions are in complete agreement with numerical results. Our
study, though limited to integrable two-level systems, points to the existence
of a universality in the scaling of the decoherence factor which is not
necessarily identical to the scaling of the defect density.Comment: 5 pages, 2 figures, Final and accepted versio
Quenching through Dirac and semi-Dirac points in optical Lattices: Kibble-Zurek scaling for anisotropic Quantum-Critical systems
We propose that Kibble-Zurek scaling can be studied in optical lattices by
creating geometries that support, Dirac, Semi-Dirac and Quadratic Band
Crossings. On a Honeycomb lattice with fermions, as a staggered on-site
potential is varied through zero, the system crosses the gapless Dirac points,
and we show that the density of defects created scales as , where
is the inverse rate of change of the potential, in agreement with the
Kibble-Zurek relation. We generalize the result for a passage through a
semi-Dirac point in dimensions, in which spectrum is linear in parallel
directions and quadratic in rest of the perpendicular directions. We
find that the defect density is given by where
and are the dynamical exponents and the correlation
length exponents along the parallel and perpendicular directions, respectively.
The scaling relations are also generalized to the case of non-linear quenching
Defect production due to quenching through a 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
, where is the characteristic time scale of quenching. We argue
that when a quantum system is quenched across a multicritical point, the
density of defects () in the final state is not necessarily given by the
Kibble-Zurek scaling form , where is the
spatial dimension, and and 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 , where the exponent determines the behavior of the
off-diagonal term of the Landau-Zener matrix at the multicritical
point. This scaling is valid not only at a multicritical point but also at an
ordinary critical point.Comment: 4 pages, 2 figures, updated references and added one figur
Design, development and thermal analysis of reusable Li-ion battery module for future mobile and stationary applications
The performance, energy storage capacity, safety, and lifetime of lithium-ion battery cells of different chemistries are very sensitive to operating and environmental temperatures. The cells generate heat by current passing through their internal resistances, and chemical reactions can generate additional, sometimes uncontrollable, heat if the temperature within the cells reaches the trigger temperature. Therefore, a high-performance battery cooling system that maintains cells as close to the ideal temperature as possible is needed to enable the highest possible discharge current rates while still providing a sufficient safety margin. This paper presents a novel design, preliminary development, and results for an inexpensive reusable, liquid-cooled, modular, hexagonal battery module that may be suitable for some mobile and stationary applications that have high charge and or discharge rate requirements. The battery temperature rise was measured experimentally for a six parallel 18650 cylindrical cell demonstrator module over complete discharge cycles at discharge rates of 1C, 2C and 3C. The measured temperature rises at the hottest point in the cells, at the anode terminal, were found to be 6, 17 and 22 °C, respectively. The thermal resistance of the system was estimated to be below 0.2 K/W at a coolant flow rate of 0.001 Kg/s. The proposed liquid cooled module appeared to be an effective solution for maintaining cylindrical Li-ion cells close to their optimum working temperature
Quenching Dynamics of a quantum XY spin-1/2 chain in presence of 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 , where 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 . 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.Comment: 8 pages, 6 figure
Quenching across quantum critical points: role of topological patterns
We introduce a one-dimensional version of the Kitaev model consisting of
spins on a two-legged ladder and characterized by Z_2 invariants on the
plaquettes of the ladder. We map the model to a fermionic system and identify
the topological sectors associated with different Z_2 patterns in terms of
fermion occupation numbers. Within these different sectors, we investigate the
effect of a linear quench across a quantum critical point. We study the
dominant behavior of the system by employing a Landau-Zener-type analysis of
the effective Hamiltonian in the low-energy subspace for which the effective
quenching can sometimes be non-linear. We show that the quenching leads to a
residual energy which scales as a power of the quenching rate, and that the
power depends on the topological sectors and their symmetry properties in a
non-trivial way. This behavior is consistent with the general theory of quantum
quenching, but with the correlation length exponent \nu being different in
different sectors.Comment: 5 pages including 2 figures; this is the published versio
Quenching along a gapless line: A different exponent for defect density
We use a new quenching scheme to study the dynamics of a one-dimensional
anisotropic spin-1/2 chain in the presence of a transverse field which
alternates between the values h+\de and h-\de from site to site. In this
quenching scheme, the parameter denoting the anisotropy of interaction (\ga)
is linearly quenched from to as \ga = t/\tau, keeping
the total strength of interaction fixed. The system traverses through a
gapless phase when \ga is quenched along the critical surface h^2 = \de^2 +
J^2 in the parameter space spanned by , \de and \ga. By mapping to an
equivalent two-level Landau-Zener problem, we show that the defect density in
the final state scales as , a behavior that has not been observed
in previous studies of quenching through a gapless phase. We also generalize
the model incorporating additional alternations in the anisotropy or in the
strength of the interaction, and derive an identical result under a similar
quenching. Based on the above results, we propose a general scaling of the
defect density with the quenching rate for quenching along a gapless
critical line.Comment: 6 Pages, 2 figures, accepted in Phys. Rev.
Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system
We discuss a technique for solving the Landau-Zener (LZ) problem of finding
the probability of excitation in a two-level system. The idea of time reversal
for the Schrodinger equation is employed to obtain the state reached at the
final time and hence the excitation probability. Using this method, which can
reproduce the well-known expression for the LZ transition probability, we solve
a variant of the LZ problem which involves waiting at the minimum gap for a
time t_w; we find an exact expression for the excitation probability as a
function of t_w. We provide numerical results to support our analytical
expressions. We then discuss the problem of waiting at the quantum critical
point of a many-body system and calculate the residual energy generated by the
time-dependent Hamiltonian. Finally we discuss possible experimental
realizations of this work.Comment: 6 pages including 3 figures; significantly expanded -- this is the
published versio
Scaffolding Case Analysis Writing: A Collaboration between Information Systems and Writing Faculty
In this paper, we present a collaboration between writing professors and an information systems (IS) professor to scaffold case analysis writing at an American English-medium branch campus in the Middle East. We describe our process for revising the professor’s writing assignment to make his expectations more explicit and for creating scaffolding materials that we delivered in classroom workshops to assist students’ pre-writing. We provide insights about the positive impact of the writing workshops on students’ writing from an end-of-semester interview with the professor and from interviews with students about their perceptions of the workshops and the personalized feedback they received
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