17,548 research outputs found
Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
We investigate a weak version of subsystem eigenstate thermalization
hypothesis (ETH) for a two-dimensional large central charge conformal field
theory by comparing the local equivalence of high energy state and thermal
state of canonical ensemble. We evaluate the single-interval R\'enyi entropy
and entanglement entropy for a heavy primary state in short interval expansion.
We verify the results of R\'enyi entropy by two different replica methods. We
find nontrivial results at the eighth order of short interval expansion, which
include an infinite number of higher order terms in the large central charge
expansion. We then evaluate the relative entropy of the reduced density
matrices to measure the difference between the heavy primary state and thermal
state of canonical ensemble, and find that the aforementioned nontrivial eighth
order results make the relative entropy unsuppressed in the large central
charge limit. By using Pinsker's and Fannes-Audenaert inequalities, we can
exploit the results of relative entropy to yield the lower and upper bounds on
trace distance of the excited-state and thermal-state reduced density matrices.
Our results are consistent with subsystem weak ETH, which requires the above
trace distance is of power-law suppression by the large central charge.
However, we are unable to pin down the exponent of power-law suppression. As a
byproduct we also calculate the relative entropy to measure the difference
between the reduced density matrices of two different heavy primary states.Comment: 28 pages, 4 figures;v2 change author list;v3 related subtleties about
weak ETH clarified; v4 minor correction to match JHEP versio
Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
We calculate various quantities that characterize the dissimilarity of
reduced density matrices for a short interval of length in a
two-dimensional (2D) large central charge conformal field theory (CFT). These
quantities include the R\'enyi entropy, entanglement entropy, relative entropy,
Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt
the method of operator product expansion of twist operators, and calculate the
short interval expansion of these quantities up to order of for the
contributions from the vacuum conformal family. The formal forms of these
dissimilarity measures and the derived Fisher information metric from
contributions of general operators are also given. As an application of the
results, we use these dissimilarity measures to compare the excited and thermal
states, and examine the eigenstate thermalization hypothesis (ETH) by showing
how they behave in high temperature limit. This would help to understand how
ETH in 2D CFT can be defined more precisely. We discuss the possibility that
all the dissimilarity measures considered here vanish when comparing the
reduced density matrices of an excited state and a generalized Gibbs ensemble
thermal state. We also discuss ETH for a microcanonical ensemble thermal state
in a 2D large central charge CFT, and find that it is approximately satisfied
for a small subsystem and violated for a large subsystem.Comment: V1, 34 pages, 5 figures, see collection of complete results in the
attached Mathematica notebook; V2, 38 pages, 5 figures, published versio
Expanding the thermodynamical potential and the analysis of the possible phase diagram of deconfinement in FL model
The deconfinement phase transition is studied in the FL model at finite
temperature and chemical potential. At MFT approximation, the phase transition
can only be the first order in the whole phase plane. By a Landau
expansion we further study the phase transition order and the possible phase
diagram of deconfinement. We discuss the possibilities of second order phase
transitions in FL model. By our analysis the cubic term in the Landau expansion
could be cancelled by the high order fluctuations. By an ansatz of the Landau
parameters, we obtain the possible phase diagram with both first and second
order phase transition including the tricritical point which is similar to that
of the chiral phase transition.Comment: 7 pages, 8 figures, submitted to Chinese Physics
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MHD-RLC discharge model and the efficiency characteristics of plasma synthetic jet actuator
Major factors affecting efficiency of plasma synthetic jet actuator (PSJA) are analyzed based on a new discharge model in the present paper. The model couples the magnetohydrodynamics (MHD) equations with the resistor–inductor–capacitor (RLC) equations, and is able to resolve the time-dependent voltage fall on the sheath region and arc region, which is critical in analyzing energy loss in the heating process. This model is integrated into the commercial CFD software by a two-equation method. Results show that in a typical capacitive discharge at microsecond scale, the maximum energy loss is the sheath energy loss, which accounts for nearly half of the discharge energy, while the radiation loss is less than 5%. The discharge time is an important parameter for the PSJA efficiency. A short discharge time less than 1 μs will effectively reduce the sheath energy loss, while a longer discharge time will decrease the thermodynamic efficiency
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