Phase diagram of a Schelling segregation model

The collective behavior in a variant of Schelling’s segregation model is characterized with methods borrowed from statistical physics, in a context where their relevance was not conspicuous. A measure of segregation based on cluster geometry is defined and several quantities analogous to those used to describe physical lattice models at equilibrium are introduced. This physical approach allows to distinguish quantitatively several regimes and to characterize the transitions between them, leading to the building of a phase diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We also establish links with ‘spin-1’ models in physics. Our approach provides generic tools to analyze the dynamics of other socio-economic systems.     

Subquantum information and computation

It is argued that immense physical resources — for nonlocal communication, espionage, and exponentially-fast computation — are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that ‘non-quantum’ or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time).     

A gentle introduction to the thermodynamics of biochemical stoichiometric networks in steady state

Reaction networks in thermodynamic equilibrium under isothermal and isobaric conditions minimize the Gibbs free energy, but chemical reactions in living organisms operate typically far from equilibrium. Currently, there is no general optimization principle for nonequilibrium systems which can be used in the analysis of biochemical networks. Motivated by the avalailabity of whole genome reconstructions of metabolic reactions, the thermodynamics of biochemical stoichiometric networks has made significant progress in the last decade. These include the consistent formulation of conservation conditions resembling Kirchhoff’s law for electrical networks. In addition, Beard and Qian suggested that the flow force relationship Δμ = RT log(J⁺/J⁻) between the forward and backward fluxes J⁺ and J⁻ and the chemical potential difference of a chemical reaction can be extended from mass action kinetics to more general reactions schemes. In this tutorial review we summarize the recent literature on reaction network thermodynamics and discuss its implications to the analysis of large biochemical systems. In addition, we discuss some recent work on flow-force relationships and global variational principles characterizing nonequilibrium steady states of reaction networks.     

Schrödinger’s Cat Meets Einstein’s Twins: A Superposition of Different Clock Times

The phenomenon of quantum superposition, which allows a physical system to exist in different states ‘simultaneously’, is one of the most bizarre notions in physics. Here we illustrate an even more bizarre example of it: a superposed state of a physical system consisting of both an ‘older’ version and a ‘younger’ version of that system. This can be accomplished by exploiting the special relativistic effect of time dilation featuring in Einstein’s famous twin paradox.     

All basic condensed matter physics phenomena and notions mirror in biology — A hypothesis,two examples and a novel prediction

A few billion years of evolutionary time and the complex process of ‘selection’ has given biology an opportunity to explore a variety of condensed matter phenomena and situations, some of which have been discovered by humans in the laboratory, that too only in extreme non-biological conditions such as low temperatures, high purity, high pressure etc., in the last centuries. Biology, at some level, is a complex and self-regulated condensed matter system compared to the ‘inanimate’ condensed matter systems such as liquid ⁴He, liquid water or a piece of graphite. In this article I propose a hypothesis that ‘all basic condensed matter physics phenomena and notions (already known and ones yet to be discovered) mirror in biology’. I explain this hypothesis by considering the idea of ‘Bose condensation’ or ‘momentum space order’ and discuss two known example of quantum magnetism encountered in biology. I also provide some new and rather speculative possibility, from light harvesting in biological photosynthesis, of mesoscopic excition condensation related phenomena at room temperature.     

Extremes of nuclear structure

With the advent of medium and large gamma detector arrays, it is now possible to look at nuclear structure at high rotational forces. The role of pairing correlations and their eventual breakdown, along with the shell effects have showed us the interesting physics for nuclei at high spins — superdeformation, shape co-existence, yrast traps, alignments and their dramatic effects on nuclear structure and so on. Nuclear structure studies have recently become even more exciting, due to efforts and possibilities to reach nuclei far off from the stability valley. Coupling of gamma ray arrays with ‘filters’, like neutron wall, charged particle detector array, gamma ray total energy and multiplicity castles, conversion electron spectrometers etc gives a great handle to study nuclei produced online with ‘low’ cross-sections. Recently we studied, nuclei in mass region 80 using an array of 8 germanium detectors in conjunction with the recoil mass analyser, HIRA at the Nuclear Science Centre and, most unexpectedly came across the phenomenon of identical bands, with two quasi-particle difference. The discovery of magnetic rotation is another highlight. Our study of light In nucleus, 107In brought us face to face with the ‘dipole’ bands. I plan to discuss some of these aspects. There is also an immensely important development — that of the ‘radioactive ion beams’. The availability of RIB, will probably very dramatically influence our ‘conventional’ concept of nuclear structure. The exotic shapes of these exotic nuclei and some of their expected properties will also be touched upon.     

Wigner distributions for finite dimensional quantum systems: An algebraic approach

We discuss questions pertaining to the definition of ‘momentum’, ‘momentum space’, ‘phase space’ and ‘Wigner distributions’; for finite dimensional quantum systems. For such systems, where traditional concepts of ‘momenta’ established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail     

Radiation-stimulated diffusion in solids

Irradiation of solids produces a microscopic nonequilibrium state in which the vibrational energy distribution function of the atoms deviates from the thermodynamically equilibrium function. Expressions are obtained for the nonequilibrium distribution function and for the frequencies of activational transitions of atoms out of a potential well. It is shown that the radiation stimulation of diffusion processes involves a deviation of the temperature dependences of the frequencies of transitions of the atoms out of positions of equilibrium from the Arrhenius law. Under subthreshold irradiation conditions the rate of diffusion processes is higher for atoms whose vibrations thermalize over long times and depends linearly on the irradiation intensity. Under above-threshold irradiation conditions the characteristics of cascade regions in solids — their sizes and the vibrational excitation energy of the atoms — can be determined by comparing the computed and experimental temperature dependences of the diffusion coefficient. Zh. Tekh. Fiz. 68, 67–72 (August 1998)     

Reply to “quantum tunneling times: A crucial test for the causal program?”

Because Bohm’s Interpretation models particles with continuous trajectories, a natural property to attribute to a Bohmian particle is atunneling time, the time it takes for a particle to pass through a barrier. We also attribute a property-a different property-named ‘tunneling time’ to Copenhagen systems, systems that do not have particles with continuous trajectories. Cushing presents a discussion of the possibility of measuring Bohmian particle tunneling time; however, as becomes clear when considering the differences between properties named ‘tunneling time,’ he incorrectly argues that if such a measurement were possible, the measurement might constitute an empirical test between the Copenhagen interpretation and Bohm’s interpretation.     

Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.     

Infinity and Newton’s Three Laws of Motion

It is shown that the following three common understandings of Newton’s laws of motion do not hold for systems of infinitely many components. First, Newton’s third law, or the law of action and reaction, is universally believed to imply that the total sum of internal forces in a system is always zero. Several examples are presented to show that this belief fails to hold for infinite systems. Second, two of these examples are of an infinitely divisible continuous body with finite mass and volume such that the sum of all the internal forces in the body is not zero and the body accelerates due to this non-null net internal force. So the two examples also demonstrate the breakdown of the common understanding that according to Newton’s laws a body under no external force does not accelerate. Finally, these examples also make it clear that the expression ‘impressed force’ in Newton’s formulations of his first and second laws should be understood not as ‘external force’ but as ‘exerted force’ which is the sum of all the internal and external forces acting on a given body, if the body is infinitely divisible.     

Random Walks and Polymers in the Presence of Quenched Disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local transition rules, and on ‘polymer models’, where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points: thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures T _c(i,L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland–Scheraga model of DNA denaturation.Conference Proceedings “Mathematics and Physics”, I.H.E.S., France, November 2005     

Self-induced transparency for ultrashort pulses propagating in a multilevel quantum medium

We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0π-, 2π-, and 4π-videosolitons are formed. It is found that 4π-videosolitons can propagate both in equilibrium media and in some nonequilibrium media, while 0π-videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2π-and qπ-pulses (0<q<1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increase in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium. Zh. éksp. Teor. Fiz. 114, 1595–1617 (November 1998)     

The Evaluation of Atomic Masses

The ensemble of experimental data on the 2830 nuclides which have been observed since the beginning of Nuclear Physics are being evaluated, according to their nature, by different methods and by different groups. The two ‘horizontal’ evaluations in which I am involved: the Atomic Mass Evaluation AME and the NUBASE evaluation belong to the class of ‘static’ nuclear data. In this tutorial lecture I will explain and discuss in detail the philosophy, the strategies and the procedures used in the evaluation of atomic masses. This revised version was published online in July 2006 with corrections to the Cover Date.     

Generalized Fock spaces,new forms of quantum statistics and their algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’, Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations.     

What is Erased in the Quantum Erasure?

In this paper, we re-examine a series of gedanken welcher Weg (WW) experiments introduced by Scully, Englert and Walther that contain the essential ideas underlying the quantum eraser. For this purpose we use the Bohm model which gives a sharp picture of the behaviour of the atoms involved in these experiments. This model supports the thesis that interference disappears in such WW experiments, even though the centre of mass wave function remains coherent throughout the experiment. It also shows exactly what it means to say ‘that the interference can be restored by manipulating the WW detectors long after the atoms have passed’. It does not support Wheeler’s notion that ‘the past is undefined and undefinable without the observation (in the present)’.     

Phenomenological dynamics: From Navier–Stokes to chiral granular gases

This paper reviews the derivation of equations for slow dynamical processes in a variety of systems, including rotating rigid rotors, crystalline solids, isotropic and nematic elastomers, gels in an isotropic fluid background, and nematic liquid crystals. It presents a recent derivation of the Leslie-Ericksen equations for the dynamics of nematic liquid crystals that clarifies the nature of the nonhydrodynamic modes in these equations. As a final example of the phenomenological approach to slow dynamical processes, it discusses the dynamics of a driven nonequilibrium system: a two-dimensional gas of chiral ‘rattlebacks’ on a vibrating substrate.     

Studies of polarization/self-depolarization and electret-type effect in AgI

A novel d.c. polarization/self-depolarization study and electret-type effect in AgI are reported. AgI pellets of varying thicknesses, placed between two blocking (graphite) electrodes, were subjected to an external d.c. potential. A state of complete polarization was attained within ∼10 min, irrespective of the sample thickness. At this state, the potential difference, developed across the sample pellet as a result of polarization/accumulation of mobile Ag⁺ ions at the bulk/negative electrode interface, was measured experimentally. The potential difference, obtained immediately after the removal of the external d.c. source, has been referred to as ‘instant peak potential (V_p)’. As soon as the external voltage source is switched off, a process of self-depolarization is initiated due to the chemical/self diffusion of polarized mobile Ag⁺ ions throughout the bulk. ‘V_p’ gives a direct information regarding the extent of mobile ion concentration (n). ‘V_p’ measurements were carried out as a function of temperature and ‘Log V_p vs 1/T’ variation was compared with the ‘Log n vs 1/T’ Arrhenius plot, reported earlier in an entirely independent study. The two variations are almost analogous. This, in turn, supported as an earlier assertion that the abrupt conductivity increase in α-AgI, after β→α-phase transition at ∼147 °C, is predominantly due to the excessive increase in ‘n’. Furthermore, it has also been revealed that the Ag⁺ ions play another unique role which led to the existence of ‘persistent polarization’ states in AgI. These states are identical to the ‘electret-type effects’, observed in a number of dielectric materials. The polarization state persisted for very long time in ‘thermally stimulated polarized’ sample. A detailed investigation of the persistence/retention of polarization in the thermally-stimulated-polarized sample is reported.     

Emerging molecular diversity from the intra-molecular Ugi reaction: iterative efficiency in medicinal chemistry

This review details a now established area within the isonitrile multi-component reaction (IMCR) field of study, namely employing bi-functional reagents in the Ugi reaction for the construction of screening sets with the additional element or even possibly ‘metric’ of enhanced ‘iterative efficiency potential’ The concept of ‘iterative efficiency’ will be briefly introduced, coupled with discussion on new synthetic routes to select bi-functional IMCR precursors and their use in the generation of pharmacologically relevant ‘molecular diversity’