Jarzynski equality for quantum stochastic maps

Jarzynski equality and related fluctuation theorems can be formulated for various setups. Such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations, i.e., for completely positive, trace-preserving maps, which preserve the maximally mixed state. We analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the Jarzynski equality. It contains a correction term due to nonunitality of the quantum map. Bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite-dimensional Hilbert space.Comment: 11 pages, one figure. Final minor changes are made. The version 4 matches the journal versio

Spin solid phases of spin 1 and spin 3/2 antiferromagnets on a cubic lattice

We study spin S=1 and S=3/2 Heisenberg antiferromagnets on a cubic lattice focusing on spin solid states. Using Schwinger boson formulation for spins, we start in a U(1) spin liquid phase proximate to Neel phase and explore possible confining paramagnetic phases as we transition away from the spin liquid by the process of monopole condensation. Electromagnetic duality is used to rewrite the theory in terms of monopoles. For spin 1 we find several candidate phases of which the most natural one is a phase with spins organized into parallel Haldane chains. For spin 3/2 we find that the most natural phase has spins organized into parallel ladders. As a by-product, we also write a Landau theory of the ordering in two special classical frustrated XY models on the cubic lattice, one of which is the fully frustrated XY model. In a particular limit our approach maps to a dimer model with 2S dimers coming out of every site, and we find the same spin solid phases in this regime as well.Comment: 15 pages, 8 figure

Numerical range for random matrices

We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius $\sqrt{2}$. Since the spectrum of non-hermitian random matrices from the Ginibre ensemble lives asymptotically in a neighborhood of the unit disk, it follows that the outer belt of width $\sqrt{2}-1$ containing no eigenvalues can be seen as a quantification the non-normality of the complex Ginibre random matrix. We also show that the numerical range of upper triangular Gaussian matrices converges to the same disk of radius $\sqrt{2}$, while all eigenvalues are equal to zero and we prove that the operator norm of such matrices converges to $\sqrt{2e}$.Comment: 23 pages, 4 figure

On certain non-unique solutions of the Stieltjes moment problem

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems

Exposure of prepubertal beef bulls to cycling females does not enhance sexual development

The objective of this study was to determine whether continuous, long-term, fenceline exposure of prepubertal beef bulls to cycling beef females reduced age at puberty and influenced the percentage of bulls that passed an initial breeding soundness examination (BSE). Bulls (Angus, N = 37; Simmental, N = 22; Hereford, N = 10; Simmental x Angus, N = 8) averaging 202 ± 21.5 d of age were given either continuous fenceline and visual exposure to cycling females (Exposed: N= 41) or no exposure (Control: N=36). Estrus was induced in cycling beef females so at least 3 females were in standing estrus each week during the 182 d of exposure to bulls. Scrotal circumference (SC), body weight, and blood samples were collected every 28 d. When bulls had SC ≥ 26 cm, semen samples were obtained monthly via electroejaculation until puberty was achieved (≥ 50 x 106 sperm/mL with at least 10% progressive motility). Behavioral observations were conducted twice monthly, once when females were in estrus and once during diestrus. Homosexual mounting, flehmen responses, and number of times near penned females were recorded for each observation period. Breeding soundness examinations were conducted when bulls averaged 364 ± 21.5 d of age. Normal sperm morphology of at least 70% and sperm motility of at least 30% were required to pass the BSE. Age, body weight, and SC at puberty did not differ between Exposed and Control bulls (320 ± 28 d and 311 ± 29 d; 466.2 ± 12.2 and 437.7 ± 13.5 kg; and 34.4 ± 2.5 cm and 34.9 ± 2.5 cm, respectively). Percentage of bulls passing their initial BSE did not differ between treatments (Exposed: 87.8%, Control: 75.0%). Treatment, month, and female estrous stage interacted (P = 0.05) to affect the number of mount attempts and flehmen responses. Exposed bulls entered the cow area more times (P < 0.001) during estrus than diestrus in months one, two and three. We concluded that bulls given 3 continuous, long-term, fenceline exposure to cycling beef females do not have enhanced sexual development