Fluctuation relation for heat exchange in Markovian open quantum systems

A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability of that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. We also argue that the probability of the violation of the second law of thermodynamics (here in the form of net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences.Comment: 5 pages, 2 figure

On the Relativistic Quantum Force

In the extension of the de-Broglie-Bohm causal quantum theory of motion to the relativistic particles, one faces with serious problems, like the problem of superluminal motion. This forces many authors to believe that there is not any satisfactory causal theory for particles of integer spin. In this paper, it is shown that the quantal behaviour is the result of direct-particle-interaction of the particle with all of its possibilities. The formulation is, then, extended to the relativistic particles of arbitrary spin. The presented theory has the following advantages. (1) It leads to a deeper understanding of the quantal behaviour. (2) It has no superluminal motion. (3) It is applicable to any spin. (4) It provides a framework for understanding the problem of creation and annihilation of particles. (5) It provides a framework for understanding the spin-statistics relationship. (6) It does not need the two fundamental assumptions of the de-Broglie-Bohm quantum theory of motion, i.e., the guiding-formula postulate and the statistical postulate.Comment: 44 pages, LaTex, no figur

Is superluminal motion in relativistic Bohm's theory observable?

We show that the problem of superluminal motion in causal, particle interpretation of bosonic fields is not observable at macroscopic distances.Comment: 9 pages, LaTex, 1 figure available upon reques

On the Chern-Yamabe flow

On a closed balanced manifold, we show that if the Chern scalar curvature is small enough in a certain Sobolev norm then a slightly modified version of the Chern-Yamabe flow~\cite{Angella:2015aa} converges to a solution of the Chern-Yamabe problem. We also prove that if the Chern scalar curvature, on closed almost-Hermitian manifolds, is close enough to a constant function in a H\"older norm then the Chern-Yamabe problem has a solution for generic values of the fundamental constant.Comment: 12 page

Heralded entangled coherent states between spatially separated massive resonators

We put forward an experimentally feasible scheme for heralded entanglement generation between two distant macroscopic mechanical resonators. The protocol exploits a hybrid quantum device, a qubit interacting with a mechanical resonator as well as a cavity mode, for each party. The cavity modes interfere on a beam-splitter followed by suitable heralding detections which post-select a hybrid entangled state with success probability 1/2. Subsequently, by local measurements on the qubits a mechanical entangled coherent state can be achieved. The mechanical entanglement can be further verified via monitoring the entanglement of the qubit pair. The setup is envisioned as a test bench for sensing gravitational effects on the quantum dynamics of gravitationally coupled massive objects. As a concrete example, we illustrate the implementation of our protocol using the current circuit QED architectures.Comment: 11 pages, 3 figure

Equivalent Conditions for Digital Covering Maps

In this paper we show that a digital $(\kappa,\lambda)-$continuous surjection $p:(E,\kappa)\rightarrow (B,\lambda)$ is a digital covering map if and only if it is a local isomorphism. Moreover, we find a loop criterion for a digital covering map to be an $n$-radius covering. Also, we show that every digitally continuous map with unique path lifting property is a digital covering map if it has no conciliator point

Improving the optomechanical entanglement and cooling by photothermal force

Cooling and Entanglement in optomechanical systems coupled through radiation pressure and photothermal force is studied. To develop the photothermal model, we derive an expression for deformation constant of the force. Exploiting linearized quantum Langevin equations we investigate dynamics of such systems. According to our analysis, in addition to separate action of radiation pressure and photothermal force, their cross correlation effect plays an important role in dynamics of the system. We also achieve an exact relation for the phonon number of the mechanical resonator in such systems, and then we derive an analytical expression for it at weak coupling limit. At strong coupling regime, we show that utilizing the photothermal pressure makes the ground state cooling more approachable. The effect of photothermal force on the optomechanical entanglement is investigated in detail. According to our exact numerical and approximate analytical studies, even though the photothermal force is naturally a dissipative force, it can improve the optomechanical entanglement both quantitatively and qualitatively.Comment: 13 pages, 5 figure

Galilean Classification of Curves

In this paper, we classify space-time curves up to Galilean group of transformations with Cartan's method of equivalence. As an aim, we elicit invariats from action of special Galilean group on space-time curves, that are, in fact, conservation laws in physics. We also state a necessary and sufficient condition for equivalent Galilean motions.Comment: 10 page

Affine Geometry of Space Curves

This paper is devoted to the complete classification of space curves under affine transformations in the view of Cartan's theorem. Spivak has introduced the method but has not found the invariants. Furthermore, for the first time, we propound a necessary and sufficient condition for the invariants. Then, we study the shapes of space curves with constant curvatures in detail and suggest their applications in physics, computer vision and image processing.Comment: 17 page

Affine Classification of n-Curves

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of Cartan's lemma and then, state a necessary and sufficient condition for classification of n--Curves.Comment: 8 pages, accepted by "vol. 13 / 2008 of the journal Balkan Journal of Geometry and Its Applications