Aspects of Puff Field Theory

We describe some features of the recently constructed "Puff Field Theory," and present arguments in favor of it being a field theory decoupled from gravity. We construct its supergravity dual and calculate the entropy of this theory in the limit of large 't Hooft coupling. We also determine the leading irrelevant operator that governs its deviation from N=4 super Yang-Mills theory.Comment: 31 pages, 1 figur

Determinant of a new fermionic action on a lattice - (I)

We investigate, analytically and numerically, the fermion determinant of a new action on a (1+1)-dimensional Euclidean lattice. In this formulation the discrete chiral symmetry is preserved and the number of fermion components is a half of that of Kogut-Susskind. In particular, we show that our fermion determinant is real and positive for U(1) gauge group under specific conditions, which correspond to gauge conditions on the infinite lattice. It is also shown that the determinant is real and positive for SU(N) gauge group without any condition.Comment: 12 pages, 7 figure

Quantum-state comparison and discrimination

We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of separate discrimination measurements on each system. In some cases with more than two possible states, the optimal strategy in minimum-error comparison is that one should infer the two systems are in different states without any measurement, implying that the discrimination strategy performs worse than the trivial "no-measurement" strategy. We present a sufficient condition for this phenomenon to happen. For two pure states with equal prior probabilities, we determine the optimal comparison success probability with an error margin, which interpolates the minimum-error and unambiguous comparison. We find that the discrimination strategy is not optimal except for the minimum-error case.Comment: 8 pages, 1 figure, minor corrections made, final versio

Stationary quantum Markov process for the Wigner function

As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase space, each particle can be treated independently. This is an improvement on earlier methods that require the whole distribution function to determine the evolution of a constituent particle. The process has branching and vanishing points, though a finite time interval can be maintained between the branchings. The procedure to perform a simulation using the process is presented.Comment: 12 pages, no figures; replaced with version accepted for publication in J. Phys. A, title changed, an example adde

Statistical mechanics and large-scale velocity fluctuations of turbulence

Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.Comment: 7 pages, accepted by Physics of Fluids (see http://pof.aip.org/

Unitary-process discrimination with error margin

We investigate a discrimination scheme between unitary processes. By introducing a margin for the probability of erroneous guess, this scheme interpolates the two standard discrimination schemes: minimum-error and unambiguous discrimination. We present solutions for two cases. One is the case of two unitary processes with general prior probabilities. The other is the case with a group symmetry: the processes comprise a projective representation of a finite group. In the latter case, we found that unambiguous discrimination is a kind of "all or nothing": the maximum success probability is either 0 or 1. We also closely analyze how entanglement with an auxiliary system improves discrimination performance.Comment: 9 pages, 3 figures, presentation improved, typos corrected, final versio

Non-Linear/Non-Commutative Non-Abelian Monopoles

Using recently proposed non-linearly realized supersymmetry in non-Abelian gauge theory corrected to the order (alpha')^2, we derive the non-linear BPS equations in the background B-field for the U(2) monopoles and instantons. We show that these non-Abelian non-linear BPS equations coincide with the non-commutative anti-self-dual equations via the Seiberg-Witten map.Comment: 9 pages, LaTe

Reconnection of Colliding Cosmic Strings

For vortex strings in the Abelian Higgs model and D-strings in superstring theory, both of which can be regarded as cosmic strings, we give analytical study of reconnection (recombination, inter-commutation) when they collide, by using effective field theories on the strings. First, for the vortex strings, via a string sigma model, we verify analytically that the reconnection is classically inevitable for small collision velocity and small relative angle. Evolution of the shape of the reconnected strings provides an upper bound on the collision velocity in order for the reconnection to occur. These analytical results are in agreement with previous numerical results. On the other hand, reconnection of the D-strings is not classical but probabilistic. We show that a quantum calculation of the reconnection probability using a D-string action reproduces the nonperturbative nature of the worldsheet results by Jackson, Jones and Polchinski. The difference on the reconnection -- classically inevitable for the vortex strings while quantum mechanical for the D-strings -- is suggested to originate from the difference between the effective field theories on the strings.Comment: 29 pages, 14 eps figures, JHEP style; references added, typos correcte

Evaluating Methods for Evaluating Instruction: The Case of Higher Education

This paper develops an original measure of learning in higher education, based on grades in subsequent courses. Using this measure of learning, this paper shows that student evaluations are positively related to current grades but unrelated to learning once current grades are controlled. It offers evidence that the weak relationship between learning and student evaluations arises, in part, because students are unaware of how much they have learned in a course. The paper concludes with a discussion of easily-implemented, optimal methods for evaluating teaching.