181 research outputs found
Nielsen complexity of coherent spin state operators
We calculate Nielsen's circuit complexity of coherent spin state operators.
An expression for the complexity is obtained by using the small angle
approximation of the Euler angle parametrisation of a general rotation.
This is then extended to arbitrary times for systems whose time evolutions are
generated by couplings to an external field, as well as non-linearly
interacting Hamiltonians. In particular, we show how the Nielsen complexity
relates to squeezing parameters of the one-axis twisted Hamiltonians in a
transverse field, thus indicating its relation with pairwise entanglement. We
further point out the difficulty with this approach for the
Lipkin-Meshkov-Glick model, and resolve the problem by computing the complexity
in the Tait-Bryan parametrisation.Comment: 11 Page
Conformal Fisher information metric with torsion
We consider torsion in parameter manifolds that arises via conformal
transformations of the Fisher information metric, and define it for information
geometry of a wide class of physical systems. The torsion can be used to
differentiate between probability distribution functions that otherwise have
the same scalar curvature and hence define similar geometries. In the context
of thermodynamic geometry, our construction gives rise to a new scalar - the
torsion scalar defined on the manifold, while retaining known physical features
related to other scalar quantities. We analyse this in the context of the Van
der Waals and the Curie-Weiss models. In both cases, the torsion scalar has non
trivial behaviour on the spinodal curve.Comment: 1+13 Page
Regularising the JNW and JMN naked singularities
We extend the method of Simpson and Visser (SV) of regularising a black hole
spacetime, to cases where the initial metric represents a globally naked
singularity. We choose two particular geometries, the Janis-Newman-Winicour
(JNW) metric representing the solution of an Einstein-scalar field system, and
the Joshi-Malafarina-Narayan (JMN) metric that represents the asymptotic
equilibrium configuration of a collapsing star supported by tangential
pressures as the starting configuration. We illustrate several novel features
for the modified versions of the JNW and JMN spacetimes. In particular, we show
that, depending on the values of the parameters involved the modified JNW
metric may represents either a two way traversable wormhole or it may retain
the original naked singularity. On the other hand, the SV modified JMN geometry
is always a wormhole. Particle motion and observational aspects of these new
geometries are investigated and are shown to posses interesting features. We
also study the quasinormal modes of different branches of the regularised
spacetime and explore their stability properties.Comment: 22 Pages, 16 Figures. Discussions adde
Disformal transformations and the motion of a particle in semi-classical gravity
The approach to incorporate quantum effects in gravity by replacing free
particle geodesics with Bohmian non-geodesic trajectories has an equivalent
description in terms of a conformally related geometry, where the motion is
force free, with the quantum effects inside the conformal factor, i.e., in the
geometry itself. For more general disformal transformations relating
gravitational and physical geometries, we show how to establish this
equivalence by taking the quantum effects inside the disformal degrees of
freedom. We also show how one can solve the usual problems associated with the
conformal version, namely the wrong continuity equation, indefiniteness of the
quantum mass, and wrong description of massless particles in the singularity
resolution argument, by using appropriate disformal transformations.Comment: 18 Pages, LaTe
Time evolution of spread complexity and statistics of work done in quantum quenches
We relate the probability distribution of the work done on a statistical
system under a sudden quench to the Lanczos coefficients corresponding to
evolution under the post-quench Hamiltonian. Using the general relation between
the moments and the cumulants of the probability distribution, we show that the
Lanczos coefficients can be identified with physical quantities associated with
the distribution, e.g., the average work done on the system, its variance, as
well as the higher order cumulants. In a sense this gives an interpretation of
the Lanczos coefficients in terms of experimentally measurable quantities. We
illustrate these relations with two examples. The first one involves quench
done on a harmonic chain with periodic boundary conditions and with nearest
neighbour interactions. As a second example, we consider mass quench in a free
bosonic field theory in spatial dimensions in the limit of large system
size. In both cases, we find out the time evolution of the spread complexity
after the quench, and relate the Lanczos coefficients with the cumulants of the
distribution of the work done on the system.Comment: 12 Pages, 1 Figur
Complexity in two-point measurement schemes
We show that the characteristic function of the probability distribution
associated with the change of an observable in a two-point measurement protocol
with a perturbation can be written as an auto-correlation function between an
initial state and a certain unitary evolved state by an effective unitary
operator. Using this identification, we probe how the evolved state spreads in
the corresponding conjugate space, by defining a notion of the complexity of
the spread of this evolved state. For a sudden quench scenario, where the
parameters of an initial Hamiltonian (taken as the observable measured in the
two-point measurement protocol) are suddenly changed to a new set of values, we
first obtain the corresponding Krylov basis vectors and the associated Lanczos
coefficients for an initial pure state, and obtain the spread complexity.
Interestingly, we find that in such a protocol, the Lanczos coefficients can be
related to various cost functions used in the geometric formulation of circuit
complexity, for example the one used to define Fubini-Study complexity. We
illustrate the evolution of spread complexity both analytically, by using Lie
algebraic techniques, and by performing numerical computations. This is done
for cases when the Hamiltonian before and after the quench are taken as
different combinations of chaotic and integrable spin chains. We show that the
complexity saturates for large values of the parameter only when the pre-quench
Hamiltonian is chaotic. Further, in these examples we also discuss the
important role played by the initial state which is determined by the
time-evolved perturbation operator.Comment: 16 Pages, 6 Figure
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