Information erasure in quantum systems

The physical cost of information erasure is considered within a new approach that regards erasure as loss of correlation between the state of an erasable quantum system and that of an enduring “referent” system holding classical information. A physical model of information erasure built on this referential picture is described in detail, and lower bounds on entropic and energetic costs are obtained from quantum dynamics and entropic inequalities alone.     

Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra

In this Letter, the “number-phase entropic uncertainty relation” and the “number-phase Wigner function” of generalized coherent states associated to a few solvable quantum systems with non-degenerate spectra are studied. We also investigate time evolution of “number-phase entropic uncertainty” and “Wigner function” of the considered physical systems with the help of temporally stable Gazeau-Klauder coherent states.     

Landauer’s limit and the physicality of information

Landauer’s lower bound on the dissipative cost of information erasure is revisited within a new physical conception of information. The notion of strong physical information is introduced, and the new conception of physical information – observer-local referential (OLR) information – is defined, shown to be strongly physical, and related to other measures that arise in physical information contexts. A generalization of Landauer’s limit is then obtained for OLR information from quantum dynamics and entropic inequalities alone. Specializations of this bound are compared and contrasted to similar bounds under conditions for which they coincide, and important distinctions between seemingly identical bounds expressed in terms of various information measures are discussed. The controversial distinction between Landauer erasure of known and unknown data – and the alleged difference between their respective erasure costs – is then explored via OLR information. This physically grounds and clarifies distinctions between known and unknown data and between unconditional and conditional erasure operations, enables a straightforward physical accounting of associated lower bounds on erasure costs, and illustrates the advantages of OLR information for resolution of controversies related to the dissipative cost of information erasure. Applications of OLR information to determination of irreversibility induced dissipation bounds in more complex computing scenarios are briefly discussed.     

Entanglement,superselection rules and supersymmetric quantum mechanics

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Is BTZ a separate superselection sector of CTMG?

We exhibit exact solutions of (positive) matter coupled to original “wrong G-sign” cosmological TMG. They all evolve to conical singularity, rather than to black hole – here negative mass – BTZ. This provides evidence that the latter constitute a separate “superselection” sector, one that unlike in GR, is not reachable by physical sources.     

Kohn’s theorem, Larmor’s equivalence principle and the Newton–Hooke group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a “relativity group” which is a one-parameter family of deformations of the standard Galilei group to the Newton–Hooke group which is a Wigner–?nönü contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn’s theorem and related results. Larmor’s theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the “Eisenhart” or “lightlike” lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdi?ka–Eardley–Nappi–Witten pp-wave solution of Einstein–Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi–Jackiw group.     

Self-organization of five species in a cyclic competition game

Cyclic competition game models, particularly the “rock–paper–scissors” model, play important roles in exploring the problem of multi-species coexistence in spatially ecological systems. We propose an extended “rock–paper–scissors” game to model cyclic interactions among five species, and find that two of the five can coexistent when biodiversity disappears, which is different from the “rock–paper–scissors” game. As the number of fingers is five, we named the new model the “fingers” game, where the thumb, forefinger, middle finger, ring finger, and little finger cyclically dominate their subsequent species and are dominated by their former species. We investigate the “fingers” model in two ways: direct simulations and nonlinear partial differential equations. An important finding is that the number of species in a cyclic competition game has an influence on the emergence of biodiversity. To be specific, the “rock–paper–scissors” model is in favor of maintaining biodiversity in comparison with the “fingers” model when the variables (population size, reproduction rate, selection rate, and migration rate) are the same. It is also shown that the mobility and reproduction rate can promote or jeopardize biodiversity.     

How random is a random vector?

Over 80 years ago Samuel Wilks proposed that the “generalized variance” of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the “Wilks standard deviation” –the square root of the generalized variance–is indeed the standard deviation of a random vector. We further establish that the “uncorrelation index” –a derivative of the Wilks standard deviation–is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: “randomness measures” and “independence indices” of random vectors. In turn, these general notions give rise to “randomness diagrams”—tangible planar visualizations that answer the question: How random is a random vector? The notion of “independence indices” yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.     

Econophysical visualization of Adam Smith’s invisible hand

Consider a complex system whose macrostate is statistically observable, but yet whose operating mechanism is an unknown black-box. In this paper we address the problem of inferring, from the system’s macrostate statistics, the system’s intrinsic force yielding the observed statistics. The inference is established via two diametrically opposite approaches which result in the very same intrinsic force: a top-down approach based on the notion of entropy, and a bottom-up approach based on the notion of Langevin dynamics. The general results established are applied to the problem of visualizing the intrinsic socioeconomic force–Adam Smith’s invisible hand–shaping the distribution of wealth in human societies. Our analysis yields quantitative econophysical representations of figurative socioeconomic forces, quantitative definitions of “poor” and “rich”, and a quantitative characterization of the “poor-get-poorer” and the “rich-get-richer” phenomena.     

On the role of symmetries in the theory of photonic crystals

We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan–Altland–Zirnbauer scheme. Of particular importance are complex conjugation C$C$ and time-reversal T$T$, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C$C$ is a “particle–hole-type symmetry” rather than a “time-reversal symmetry” if one considers the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schrödinger equation; The symmetry which implements physical time-reversal is a “chiral-type symmetry”. We justify by an analysis of the band structure why the first-order formalism seems to be more advantageous than the second-order formalism. Moreover, based on the Schrödinger formalism, we introduce a class of effective (tight-binding) models called Maxwell–Harper operators. Some considerations about the breaking of the “particle–hole-type symmetry” in the case of gyrotropic crystals are added at the end of this paper.     

Comment on “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al.

The purpose of this comment is to point out the inappropriate assumption of “3αH>1$3\alpha H>1$” and two problems in the proof of “Theorem 3.1” in section 3 of the paper “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al. [H. Gu, J.R. Liang, Y. X. Zhang, Time-changed geometric fractional Brownian motion and option pricing with transaction costs, Physica A 391 (2012) 3971–3977]. Then we show the two problems will be solved under our new assumption.     

Negative probabilities and information gain in weak measurements

We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. The probabilities inferred from weak measurements change along with the coupling strength; and the true probabilities can be obtained when the coupling is strong enough. By calculating the information gain of the measuring device about which path the particles pass through, we show that the “negative probabilities” only emerge for cases when the information gain is little due to very weak coupling between the measuring device and the particles. When the coupling strength increases, we can unambiguously determine whether a particle passes through a given path every time, hence the average shifts always represent true probabilities, and the strange “negatives probabilities” disappear.     

Erratum to “Model for domain wall avalanches in ferromagnetic thin films” [Physica A, 390 (2011) 4192–4197]

We detail typing corrections in the paper “Model for domain wall avalanches in ferromagnetic thin films”, R.C. Buceta, D. Muraca, Physica A, 390 (2011) 4192–4197.     

Introducing a Green–Volterra series formalism to solve weakly nonlinear boundary problems: Application to Kirchhoff's string

This paper introduces a formalism which extends that of “Green's function” and that of “the Volterra series”. These formalisms are typically used to solve, respectively, linear inhomogeneous space–time differential equations in physics and weakly nonlinear time-differential input-to-output systems in automatic control. While Green's function is a space–time integral kernel which fully characterizes a linear problem, the Volterra series expansions involve a sequence of multi-variate time integral kernels (of convolution type for time-invariant systems). The extension proposed here consists in combining the two approaches, by introducing a series expansion based on multi-variate space–time integral kernels. This series allows the representation of the space–time solution of weakly nonlinear boundary problems excited by an “input” which depends on space and time.     

Identification of structural systems with full characteristic matrices under single point excitation

The aim of “System Identification” is to determine modal and system properties of structural systems. This is while in “Damage Detection”, the identification of system characteristic matrices is as important as or even more important than the identification of frequency characteristics. Because of various constraints – i.e. difficulties in force excitation of structures due to their large size, geometry, and location – in practice only single excitation and partial measurement, at selected degrees of freedom, is possible. In this paper, a single dynamic load was applied to identify a structural system only along one of the degrees of freedom of the structure. Further, responses corresponding to a few degrees of freedom were also measured. To identify a system with this sort of restricted information, a new approach was introduced enabling identification of the structure?s parameters of mass, damping and stiffness. Taking into account the significant effect of noise reduction in improving system identification accuracy levels, a noise reduction technique was also proposed. The accuracy of the method was also assessed against noise level and location of single excitation. It was shown that as noise level increases, identification errors will also increase (less than 3.5 percent). It was further observed that applying single force at the first storey of the flexural structure would yield the lowest error levels in the identification results. Later, the method?s efficiency and precision were examined through the application of a “closed loop solution” to a six-storey flexural structure, and a four-span Pratt truss. The obtained results showed that the proposed method could act as an effective model in identification of system properties.     

From shape to randomness: A classification of Langevin stochasticity

The Langevin equation–perhaps the most elemental stochastic differential equation in the physical sciences–describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output–based on the shape of the Langevin equation’s potential field.     

Erratum to “Scaling properties of the Baxter–Wu model” [Physica A 390 (2011) 3369–3384]

We detail numerical corrections for the paper “Scaling properties of the Baxter–Wu model”, Velonakis, I.N., Martinos, S.S., Physica A, 390 (2011) 3369–3384.     

Weak measurement and Bohmian conditional wave functions

It was recently pointed out and demonstrated experimentally by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be “directly measured” using weak measurement. Here it is shown that if this same technique is applied, with appropriate post-selection, to one particle from a perhaps entangled multi-particle system, the result is precisely the so-called “conditional wave function” of Bohmian mechanics. Thus, a plausibly operationalist method for defining the wave function of a quantum mechanical sub-system corresponds to the natural definition of a sub-system wave function which Bohmian mechanics uniquely makes possible. Similarly, a weak-measurement-based procedure for directly measuring a sub-system’s density matrix should yield, under appropriate circumstances, the Bohmian “conditional density matrix” as opposed to the standard reduced density matrix. Experimental arrangements to demonstrate this behavior–and also thereby reveal the non-local dependence of sub-system state functions on distant interventions–are suggested and discussed.