Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements

The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: ``singlet weights'', or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart.

Blockchain as a method of resolving hold-up problem

The hold-up problem is a form of opportunistic behavior of contractual partners. It occurs when the optimal volume and structure of transactions cannot be defined with ex ante certainty. The consequence of the hold-up problem is that, once a contractual relationship has been established, one of the parties seeks to modify the distribution of benefits in such a way that it has a higher level of profit from the contract than is justified by the contractual investments it has made. The paper examines the potential of the Blockchain concept to, applied as a framework of "smart" contracts, contribute to the elimination or reduce opportunities for the emergence of a hold-up situation. The Blockchain concept with its characteristics (transparency, protection of data integrity, shareability) deploys the foregoing potential in three ways: by witnessing the transaction via the Blockchain; ensuring the execution of a (by Blockchain certified) transaction; by verifying transactions through a decentralized system that replaces verification by third parties (courts or arbitration). Consequently, the Blockchain concept for storing and managing information substitutes the role played by the institute of trust in the classical ("analog") legal relationship.

Motion of a particle in three-dimensional fields

In the central field, the energy and angular momentum are conserved. It allows for the reduction of this problem to the problem of the motion of the particle in the effective one-dimensional field. Here the motion of a particle in Coulomb field or in the field of the isotropic harmonic oscillation with small perturbations are the most important ones. The authors discuss how the motion of a particle in the given central field can be described qualitatively for different values of the angular momentum and of the energy. Several problems deal with the motion of a particle in the Coulomb field under influence of weak constant uniform electric or magnetic fields (the classical analog of the Stark or Zeeman effect). In addition, the authors consider the motion of a charged particle in the field of the magnetic monopole and magnetic dipole. The motion of the Earth–Moon system in the field of the Sun is considered in some approximation. The displacement of the Coulomb orbit under the influence of a small force of radiation damping.

Motion of a particle in three-dimensional fields

In the central field, the energy and angular momentum are conserved. It allows for the reduction of this problem to the problem of the motion of the particle in the effective one-dimensional field. Here the motion of a particle in Coulomb field or in the field of the isotropic harmonic oscillation with small perturbations are the most important ones. The authors discuss how the motion of a particle in the given central field can be described qualitatively for different values of the angular momentum and of the energy. Several problems deal with the motion of a particle in the Coulomb field under influence of weak constant uniform electric or magnetic fields (the classical analog of the Stark or Zeeman effect). In addition, the authors consider the motion of a charged particle in the field of the magnetic monopole and magnetic dipole. The motion of the Earth–Moon system in the field of the Sun is considered in some approximation. The displacement of the Coulomb orbit under the influence of a small force of radiation damping.

Analysis of memristor-based differentiating circuit

Purpose The purpose of this paper is to propose a detailed analysis of a memristor-based differentiating circuit with buffering amplifier, a capacitor and a memristor. Design/methodology/approach The analyzed circuit is based on a resistor–capacitor differentiating scheme together with a buffering operational amplifier. In the proposed circuit, the resistor is replaced by a memristor element. Findings The considered circuit and its classical analog are investigated using a rectangular pulse sequence as input signal. A comparison between the derived results is made. An advantage of the proposed memristor circuit is the shortened duration, i.e. higher localization, of the output pulses of rectangular input pulses to be derived. Originality/value Differentiating circuits are important modules in radio-electronics. Because of their widespread usage, it is of higher interest that their new potential schematic realizations are analyzed. For the computer simulations, a previously proposed modified nonlinear memristor model is used. Several of the best and widely used basic memristor models are applied as well.

A Noncommutative Model of Cosmology with Two Metrics

We propose a bicosmology model which reduces to the classical analog of noncommutative quantum mechanics. From this point of view, one of the sources in the so modified Friedmann-Robertson- Walker equations is a kind of dark energy governed by a Chapligyn-like equation of state. The parameters of noncommutativity θ and B are interpreted in terms of the Planck area and a magnetic-like field, which presumably acts as a seed for magnetogenesis.

Classical analog to the Airy wave packet

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets – with an infinite and restricted distribution of velocities of particles – and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behaviour (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics, which provides the closest analogy, is also presented.