Urgency is a non-monotonic function of pulse rate

Urgency is a non-monotonic function of pulse rate

Urgency is a non-monotonic function of pulse rate

Urgency is a non-monotonic function of pulse rate

Holographic entanglement of purification near a critical point

In the presence of finite chemical potential $$\mu $$ μ , we holographically compute the entanglement of purification in a $$2+1$$ 2 + 1 - and $$3+1$$ 3 + 1 -dimensional field theory and also in a $$3+1$$ 3 + 1 -dimensional field theory with a critical point, at which a phase transition takes place. We observe that compared to $$2+1$$ 2 + 1 - and $$3+1$$ 3 + 1 -dimensional field theories, the behavior of entanglement of purification near critical point is different and it is not a monotonic function of $$\frac{\mu }{T}$$ μ T where T is the temperature of the field theory. Therefore, the entanglement of purification distinguishes the critical point in the field theory. We also discuss the dependence of the holographic entanglement of purification on the various parameters of the theories. Moreover, the critical exponent is calculated.

Quenched free energy in random matrix model

We compute the quenched free energy in the Gaussian random matrix model by directly evaluating the matrix integral without using the replica trick. We find that the quenched free energy is a monotonic function of the temperature and the entropy approaches log N at high temperature and vanishes at zero temperature.

Models for the BPS Berry connection

Motivated by the Nahm’s construction, in this paper, we present a systematic construction of Schrödinger Hamiltonians for a spin-1/2 particle where the Berry connection in the ground-state sector becomes the Bogomolny–Prasad–Sommerfield (BPS) monopole of SU(2) Yang–Mills–Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.

The Relativistic Boltzmann Equation and Two Times

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ . If t ( τ ) increases with τ , the worldline may be associated with a normal particle, but if it is decreasing in τ , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.

Some integral inequalities for operator monotonic functions on Hilbert spaces

Let f be an operator monotonic function on I and A, B∈I (H), the class of all selfadjoint operators with spectra in I. Assume that p : [0.1], →ℝ is non-decreasing on [0, 1]. In this paper we obtained, among others, that for A ≤ B and f an operator monotonic function on I,\matrix{0 \hfill & { \le \int\limits_0^1 {p\left( t \right)f\left( {\left( {1 - t} \right)A + tB} \right)dt - \int\limits_0^1 {p\left( t \right)dt\int\limits_0^1 {f\left( {\left( {1 - t} \right)A + tB} \right)dt} } } } \hfill \cr {} \hfill & { \le {1 \over 4}\left[ {p\left( 1 \right) - p\left( 0 \right)} \right]\left[ {f\left( B \right) - f\left( A \right)} \right]} \hfill \cr }in the operator order.Several other similar inequalities for either p or f is differentiable, are also provided. Applications for power function and logarithm are given as well.