Review: Gas of Wormholes: A Possible Ground State of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a "gas" of wormholes of mass m _p, the Planck mass (m _p 10¹⁹ GeV) and average distance l _p, the Planck length a _p(a _p 10^–33 cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l _p, the Planck lattice.     

The time arrow in a Planck gas

In this paper the quantum heat transport equation (QHT) is applied to the study of thermal properties of Planck gas, i.e., a gas of massive particles with mass equal to the Planck massM _P = (łc/G)^1/2 and whose relaxation time equals the Planck timeτ _p = (łG/c ⁵)^1/2. The quantum of thermal energy for a Planck gas,E ^Planck = 10¹⁹GeV, and the quantum thermal diffusion coefficientD ^Planck = (ħG/c)^1/2 are calculated. Within the framework of QHT the thermal phenomena in a Planck gas can be divided into two classes: for a time period shorter thanτ _p , the time reversal symmetry holds and for a time period longer thanτ _p , time symmetry is broken, i.e., a time arrow is created.     

Transport relaxation time and quantum lifetime in selectively doped GaAs/AlAs heterostructures

Low-temperature dependences of the transport relaxation time (τ_tr) and quantum lifetime (τ_q) on the density of the two-dimensional electron gas (n _e ) in GaAs quantum wells with AlAs/GaAs lateral superlattice barriers have been studied. An exponential increase in the quantum lifetime with increasing electron density has been observed. It has been shown that the sharp increase in the quantum lifetime correlates with the appearance of X electrons in the AlAs/GaAs lateral superlattice barriers. It has been established that the ratio of the transport relaxation time to the quantum lifetime in the studied structures nonmonotonically depends on the density: the ratio τ_tr/τ_q first increases linearly with n _e and then decreases. This behavior is not described by the existing theories.     

Weak Coupling and Continuous Limits for Repeated Quantum Interactions

We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ²τ → 0 and the critical case λ²τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a non-trivial invariant sub-algebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model whose asymptotic effective evolution is generated by this Lindblad operator.     

Obtaining Multimode Entangled State Representation by Generalized Radon Transformation of the Wigner Operator

In a preceding paper (Fan and Lv in J. Math. Phys. 50:102108, 2009), the phase-space integration corresponding to the straight line characteristic of two different real parameters λ,τ over the Wigner operator (i.e. the Radon transformation) leads to pure-state density operator |u〉 _{λ,τ  λ,τ} 〈u|, where |u〉 _λ,τ is just the coordinate-momentum intermediate representation. In this work we show that generalized Radon transformation of the Wigner operator yields multimode density operator of continuum variables. This provides us with a new approach for obtaining multimode entangled state representation. The Weyl ordering of the Wigner operator is used in our discussions.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_ϕ)⁻¹ with the dwell time τ_D through the cavity and the dephasing rate τ _ϕ ⁻¹ , we find an exponential suppression of weak localization by a factor of ∝ exp[− /τ_ϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F. The text was submitted by the authors in English.     

Nonlinear and quantum origin of doubly infinite family of modified addition laws for fourmomenta

We show that infinite variety of Poincaré bialgebras with nontrivial classicalr-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincaré bialgebras to quantum Poincaré groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition law in any order of dimensionfull deformation parameterλ (from physical reasons we can putλ=λ _p whereλ _p is the Planck length). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of basis in Poincaré algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct. In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can help to resolve the problem of consistent passage to macroscopic classical limit. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. Supported by KBN grant 5PO3B05620     

Quantum de Sitter algebra and some possible applications in cosmology

I summarize results recently obtained in collaboration with Amelino-Camelia, Bruno and Mandanici (preprint University of Rome “La Sapienza”, August, 2005) that concern an analysis of the path of a massless particle in a q-de Sitter space-time and an approximation scheme suitable for the corresponding analysis in a quantum FRW Universe. On the basis of some arguments in the quantum-gravity literature, the q deformation parameter is assumed to depend on both the Planck scale and the curvature, leading to results that are significantly different from those of other studies of Planck-scale effects in cosmology, where the possibility of an interplay between curvature and Planck scale was ignored. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

The Scaling Limit Geometry of Near-Critical 2D Percolation

We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = p _c+λδ^1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = p _c, based on SLE ₆. It combines the continuum nonsimple loop process describing the full scaling limit at criticality with a Poissonian process for marking double (touching) points of that (critical) loop process. The double points are exactly the continuum limits of “macroscopically pivotal” lattice sites and the marked ones are those that actually change state as λ varies. This structure is rich enough to yield a one-parameter family of near-critical loop processes and their associated connectivity probabilities as well as related processes describing, e.g., the scaling limit of 2D minimal spanning trees.     

Laser dye stability. Part 5

Photodegradation parameters that relate bleaching and absorption at the lasing wavelength λ_l have been examined for over 30 different coumarin and quinolone laser dyes in a number of solvents. Quinolone dyes were found to bleach faster than the coumarin dyes. The effect of chemical substituents was found to affect bleaching of the coumarin dyes only to a small (20%) extent in ethanol. The major effect of chemical substituents was in the conversion of a dye to products absorbing at λ_l. Effects of solvent, cover gas, and changes in fluorescent quantum yields are discussed. Of particular interest is the photodegradation parameterA, the ratio of the percent absorption at λ_l to the total input energy per dm³. Combined with τ, the total input energy per dm³ required for a laser to reach half its original intensity, it was found thatAτ=1.2±0.9 for all of the dyes independent of dye concentration in all of the solvents tested. It appears that where bleaching of the dye is only of the order of 10–20%, the absorption at λ_l is 1.2% when our dye laser has reached one-half of its initial output. It is consequently possible to estimate τ values of new dyes by the use ofA terms through the relationshipA ₁τ₁=A ₂τ₂ where τ₁ of Dye 1 has been calibrated in the same dye laser system.     

Colored Noise Enhanced Stability in a Tumor Cell Growth System Under Immune Response

In this paper, we investigate a mathematical model for describing the growth of tumor cell under immune response, which is driven by cross-correlation between multiplicative and additive colored noises as well as the nonzero cross-correlation in between. The expression of the mean first-passage time (MFPT) is obtained by virtue of the steepest-descent approximation. It is found: (i) When the noises are negatively cross-correlated (λ<0), then the escape is faster than in the case with no correlation (λ=0); when the noises are positively cross-correlated (λ>0), then the escape is slower than in the case with no correlation. Moreover, in the case of positive cross-correlation, the escape time has a maximum for a certain intensity of one of the noises, i.e., the maximum for MFPT identifies the noise enhanced stability of the cancer state. (ii) The effect of the cross-correlation time τ ₃ on the MFPT is completely opposite for λ>0 and λ<0. (iii) The self-correlation times τ ₁ and τ ₂ of colored noises can enhance stability of the cancer state, while the immune rate β can reduce it.     

Influence of quantum fluctuations on the Néel temperature of a dilute two-dimensional anisotropic antiferromagnet

A quantum Monte Carlo procedure is used to calculate the energy, sublattice magnetization, Néel temperature, and the slopes of the S=[1/T _N(x=0)]dT _N(x)/dx curves as functions of the hole concentration and the exchange anisotropy Δ=1−J _x,y/J _z in the Heisenberg model with anisotropic negative interactions between nearest neighbors in a square lattice with dilution among the lattice sites. The slope diverges in the limit Δ→0: S∼ln(6.5/Δ). Fiz. Tverd. Tela (St. Petersburg) 39, 898–900 (May 1997)     

Kinematical Reduction of Spatial Degrees of Freedom and Holographic Relation in Yang’s Quantized Space-Time Algebra

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. S. Tanaka is an Em. Professor of Kyoto University.     

Research on the Dynamic Problems of 3D Cross Coupling Quantum Harmonic Oscillator by Virtue of Intermediate Representation |<Emphasis Type="Italic">x</Emphasis>〉<Subscript><Emphasis Type="Italic">λ</Emphasis>,<Emphasis Type="Italic">ν</Emphasis></Subscript>

The intermediate representation (namely intermediate coordinate-momentum representation) |x〉 _λ,ν are introduced and employed to research the expression of the operator in intermediate representation |x〉 _λ,ν . The systematic Hamilton operator of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ,ν,τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator |x〉 _{λ,ν λ,ν} 〈x|, and the Radon transformation of Wigner function is just a margin distribution.     

Noncommutative space-time models

The FRT quantum Euclidean spaces O _q ^N are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant-curvature spaces are introduced as spheres in the quantum Cayley-Klein spaces. For N = 5 part of them is interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Analytical time-like geodesics in Schwarzschild space-time

Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r = r(λ), t = t(χ), and τ= τ (χ), where λ is the true anomaly and χ is a parameter along the orbit. A very simple relation between λ and χ is also shown. These solutions are very useful for modelling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately.     

Ground state structure of some double-λ hypernuclei by a three-body model using a simple coordinate space approach

New experimental data on the binding energyB _λλ of_λλ6He, reported very recently, come up with the valuesB _λλ = 725 ±0.14 MeV and ΔB_λλ = 101 ±0.2 MeV which are substantially lower than the old dataB _λλ = 109 ±0.8 MeV and ΔB_λλ = 4.7±10 MeV in use in literature since 1966. In view of the new data we decided to undertake a re-study of the _λλ ⁶ He hypernucleus using the same three-body model (α-λ-λ) with a simple coordinate space variational approach which was employed earlier with the old data on_λλ/6He. After fitting different λ-λ potentials to the new data of _λλ ⁶ He we have applied our method to study some double-λ hypernuclei in light, medium and heavy mass regions and have determined the structural quantities like Bλλ, the r.m.s. values of core-λ (〈r_core-λ〉〉) and λ-λ (〈r_λ-λ〉〉) distances theoretically. The core-λ interaction considered is of Woods-Saxon type. The strength and the range of the core-A potential have been adjusted to reproduce the λ-binding energy(B _λ) . These are in good agreement with the relativistic mean field (RMF) results. Our study shows that the λ-λ bonding energy ΔB_λλ decreases with increasing mass number from _λλ ¹⁰ Be to _λλ ²¹⁰ Pb of a double-A hypernucleus     

Submillimetric cyclotron resonance linewidths and electron relaxation time in copper

For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH _c=m ^* cω/e is rather high (typically 200 KG), so subharmonicsH _c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω _cτ≧50 (ω _c=eH/m ^* c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m ^* is a minimum andτ=1.8×10⁻¹⁰ s.     

Quantum Instantons with Classical Moduli Spaces

 We introduce a quantum Minkowski space-time based on the quantum group SU(2) _q extended by a degree operator and formulate a quantum version of the anti-self-dual Yang-Mills equation. We construct solutions of the quantum equations using the classical ADHM linear data, and conjecture that, up to gauge transformations, our construction yields all the solutions. We also find a deformation of Penrose's twistor diagram, giving a correspondence between the quantum Minkowski space-time and the classical projective space ℙ³. Received: 10 May 2002 / Accepted: 10 January 2003 Published online: 5 May 2003 Communicated by L. Takhtajan