On Time

This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely, the classically equivalent Jacobi action and gravity coupled to matter. It also serves as a timely introduction by examples to the classical and quantum BV-BFV formalism as well as to the AKSZ method.     

Traversal time in periodically loaded waveguides

We derive general expressions for the transmission coefficient and the traversal time in waveguides periodically loaded with dielectric slabs. We apply the results to resonant tunneling between two regions below cut-off, with exponentially decaying modes. At the resonant frequencies, we found a relationship between the traversal time and the lifetime. We also study the photonic band gap in a periodic quarter wavelength structure. As in several experiments, we found superluminal velocities.     

On Time Dynamics of Coagulation-Fragmentation Processes

We establish a characterization of coagulation-fragmentation processes, such that the induced birth and death processes depicting the total number of groups at time t≥0 are time homogeneous. Based on this, we provide a characterization of mean-field Gibbs coagulation-fragmentation models, which extends the one derived by Hendriks et al. As a by-product of our results, the class of solvable models is widened and a question posed by N. Berestycki and Pitman is answered, under restriction to mean-field models.     

On the Boil-Off Time of Probe Surfaces in Plasmas

The time required for the melting of the surface of a glass-insulated probe inserted in a plasma is computed including the influence of plasma mass motion. This effect is relevant for probe measurements in moving current sheaths of electrical gas discharges. For dense plasma focus experiments, it is shown that the time of formation of a transition layer of evaporated material is shorter than the ion relaxation time in the plasma and the transit time of the current sheath by the probe position.     

Traversal time for Dirac particles through a potential barrier

A traversal time that has no problem of superluminality was advanced for particles to tunnel through potential barriers in the non‐relativistic quantum theory in a previous paper by C.‐F. Li and Q. Wang, Physica B 296 (2001) 356. This time is generalized in this paper to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non‐relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.     

On the Distribution of Long-Term Time Averages on Symbolic Space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in ^d are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results.     

On Time Scales of Intrinsic Oscillations in the Climate System

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~60 years to ~1000 years, from the longer time-scale periodicities (20,000 year+) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.     

On the Relation Between Time Representations and Inner Product Spaces

Stable states (particles), ghosts and unstable states (particles) come with different types of time representations in unitary groups—definite or indefinite. These representations are discussed with respect to the induced inner product spaces as extensions of Hilbert spaces. Unstable particles with their decay channels are treated as higher dimensional probability collectives.     

On the Time Fractional Modulation for Electron Acoustic Shock Waves

Nonlinear features of electron-acoustic shock waves are studied.The Burgers equation is derived and converted to the time fractional Burgers equation by Agrawal's method.Using the Adomian decomposition method,the shock wave solutions of the time fractional Burgers equation are constructed.The effect of time fractional parameter on the shock wave properties in auroral plasma is investigated.     

On the Sharpness of Localization of Individual Events in Space and Time

The concept of event provides the essential bridge from the realm of virtuality of the quantum state to real phenomena in space and time. We ask how much we can gather from existing theory about the localization of an event and point out that decoherence and coarse graining—though important—do not suffice for a consistent interpretation without the additional principle of random realization.     

On the Hamiltonian of the Cubic Boson Selfinteraction in Four Dimensional Space Time

In four dimensional space time a boson field with cubic selfinteraction is considered. It is shown, that if a space cutoff function is included in the interaction term, the renormalized Hamiltonian H_ren exists as a densely defined symmetric operator.     

On the Essential Features of Metastability: Tunnelling Time and Critical Configurations

We consider Metropolis Markov chains with finite state space and transition probabilities of the form $$P(\eta ,\eta ')=q(\eta ,\eta ')e^{- \beta [H(\eta ') - H(\eta)]_+}$$ for given energy function H and symmetric Markov kernel q. We propose a simple approach to determine the asymptotic behavior, for large β, of the first hitting time to the ground state starting from a particular class of local minima for H called metastable states. We separate the asymptotic behavior of the transition time from the determination of the tube of typical paths realizing the transition. This approach turns out to be useful when the determination of the tube of typical paths is too difficult, as for instance in the case of conservative dynamics. We analyze the structure of the saddles introducing the notion of “essentiality” and describing essential saddles in terms of “gates.” As an example we discuss the case of the 2D Ising Model in the degenerate case of integer ${\tfrac{{2j}}{h}}$ .     

On Lambda and Time Operators: the Inverse Intertwining Problem Revisited

An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage, based on non-unitary similarity transformations Λ that intertwine reversible dynamics and irreversible ones. This would advocate the idea that irreversible behavior would originate at the microscopic level. Reversible evolution with an internal time operator have the intertwining property. Recently the inverse intertwining problem has been answered in the negative, that is, not every unitary evolution allowing such Λ-transformation has an internal time. This work contributes new results in this direction.     

On Hot Bangs and the Arrow of Time in Relativistic Quantum Field Theory

 A recently proposed method for the characterization and analysis of local equilibrium states in relativistic quantum field theory is applied to a simple model. Within this model states are identified which are locally (but not globally) in thermal equilibrium and it is shown that their local thermal properties evolve according to macroscopic equations. The largest space–time regions in which local equilibrium states can exist are timelike cones. Thus, although the model does not describe dissipative effects, such states fix in a natural manner a time direction. Moreover, generically they determine a distinguished space–time point where a singularity in the temperature (a hot bang) must have occurred if local equilibrium prevailed thereafter. The results illustrate how the breaking of the time reflection symmetry at macroscopic scales manifests itself in a microscopic setting. Received: 17 January 2003 / Accepted: 5 March 2003 Published online: 17 April 2003 Communicated by H. Araki and K. Fredenhagen     

On the Time Dependence of the Rate of Convergence Towards Hartree Dynamics for Interacting Bosons

Journal of Statistical Physics - We consider interacting N-Bosons in three dimensions. It is known that the difference between the many-body Schrödinger evolution in the mean-field regime and...     

On Calculating the Stopping Time of a Cylindrical Body Rotating in a Viscous Continuum and the Time of Entrainment of a Coaxial External Cylinder

The velocity distribution in the vicinity of the surface of an axisymmetric body rotating in a viscous medium at frequency ω directed along its axis is determined. The dissipative function has been calculated and used for deriving the equation of motion, from which an analytic expression for the stopping time of the body (until its complete stoppage) is obtained. The time of entrainment of an external stationary cylinder coaxial with the body is calculated by solving the time-dependent Navier–Stokes equation.     

On the Relationship Between Macroscopic and Microscopic Time Constants in gas Discharges

The complicated relationship between macroscopic and microscopic time constants in gas discharges was given on the basis of the theory of the positive column of glow discharges.     

On the Problem of Emergence of Classical Space—Time: The Quantum-Mechanical Approach

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles.