Natural Cutoff Research Articles

Quantum criticality and superconductivity in quasi-two-dimensional Dirac electronic systems

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T ≠ 0 , in the case of a local interaction, when the theory must be renormalized and also in the situation where a natural physical cutoff is present in the system. In both cases, at T = 0 , we find a quantum phase transition connecting the normal and SC phases at a certain critical coupling. The phase structure is shown to be robust against quantum fluctuations. The SC gap is determined for T = 0 and T ≠ 0 , both with and without a physical cutoff and the interplay between the gap and the SC order parameter is discussed. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high- T c cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high- T c superconductivity.

The Casimir effect in the presence of a minimal length

Large extra dimensions could lower the Planck scale to experimentally accessible values. Not only is the Planck scale the energy scale at which effects of modified gravity become important. The Planck length also acts as a minimal length in nature, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime.In this Letter we examine the influence of the minimal length on the Casimir energy between two plates.

Natural cutoff in Lévy flights caused by dissipative nonlinearity

Lévy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations Lévy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to Lévy noise can be regularized by nonlinear friction, leading to a natural cutoff in the velocity distribution and finite velocity variance.

Perturbative, Non-Supersymmetric Completions of the Little Higgs

The little Higgs mechanism produces a light 100 GeV Higgs while raising the natural cutoff from 1 TeV to 10 TeV. We attempt an iterative little Higgs mechanism to produce multiple factors of 10 between the cutoff and the 100 GeV Higgs mass in a perturbative theory. In the renormalizable sector of the theory, all quantum corrections to the Higgs mass proportional to mass scales greater than 1 TeV are absent -- this includes quadratically divergent, log-divergent, and finite loops at all orders. However, even loops proportional to scales just a factor of 10 above the Higgs (or any other scalar) mass come with large numerical factors that reintroduce fine-tuning. Top loops, for example, produce an expansion parameter of not 1/(4 pi) but 1/5. The geometric increase in the number of fields at higher energies simply exacerbates this problem. We build a complete two-stage model up to 100 TeV, show that direct sensitivity of the electroweak scale to the cutoff is erased, and estimate the tuning due to large numerical factors. We then discuss the possibility, in a toy model with only scalar and gauge fields, of generating a tower of little Higgs theories and show that the theory quickly becomes a large-N gauge theory with ~ N fundamental scalars. We find evidence that at least this toy model could successfully generate light scalars with an exponentially large cutoff in the absence of supersymmetry or strong dynamics. The fine-tuning is not completely eliminated, but evidence suggests that this result is model dependent. We then speculate as to how one might marry a working tower of fields of this type at high scales to a realistic theory at the weak scale.

THE MINIMAL LENGTH AND LARGE EXTRA DIMENSIONS

Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must appear. Little is known about the fundamental theory valid at Planckian energies, except that it necessarily seems to imply the occurrence of a minimal length scale, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime. Motivated by String Theory, the models of large extra dimensions lower the Planck scale to values soon accessible. These models predict a vast number of quantum gravity effects at the lowered Planck scale, among them the production of TeV-mass black holes and gravitons. Within the extra dimensional scenario, the minimal length also comes into the reach of experiment and sets a fundamental limit to short distance physics. We review the status of Planck scale physics in these effective models.

On non-extensive statistics, chaos and fractal strings

Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics (with a non-additive q-entropy) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such a class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum, which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature (Kelvin) corresponds to zero dimensions (energy) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum groups and number theory are briefly discussed within the framework of fractal strings and branes.

Weakly coupled metastable graviton

A graviton of a nonzero mass and decay width propagates five physical polarizations. The question of interactions of these polarizations is crucial for viability of models of massive/metastable gravity. This question is addressed in the context of the DGP model of a metastable graviton. First, we argue that the well-known breakdown of a naive perturbative expansion at a low scale is an artifact of the weak-field expansion itself. Then, we propose a different expansion---the constrained perturbation theory---in which the breakdown does not occur and the theory is perturbatively tractable all the way up to its natural ultraviolet cutoff. In this approach the couplings of the extra polarizations to matter and their self-couplings appear to be suppressed and should be neglected in measurements at subhorizon scales. The model reproduces results of General Relativity at observable distances with high accuracy, while predicting deviations from them at the present day horizon scale.

Suppressed black hole production from minimal length

Large extra dimensions lower the Planck scale to values soon accessible. Motivated by string theory, the models of large extra dimensions predict a vast number of new effects in the energy range of the lowered Planck scale, among them the production of TeV-mass black holes. But not only is the Planck scale the energy scale at which effects of modified gravity become important. String theory as well as non-commutative quantum mechanics suggest that the Planck length acts a minimal length in nature, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime. The minimal length effects thus become important in the same energy range in which the black holes are expected to form.In this Letter we examine the influence of the minimal length on the expected production rate of the black holes.

Fields with finite information density

The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.

Bare vs effective pairing forces: A microscopic finite-range interaction for Hartree-Fock-Bogolyubov calculations in coordinate space

We propose a microscopic effective interaction to treat pairing correlations in the $^{1}S_{0}$ channel. It is introduced by recasting the gap equation written in terms of the bare force into a fully equivalent pairing problem. Within this approach, the proposed interaction reproduces the pairing properties provided by the realistic AV18 force very accurately. Written in the canonical basis of the actual Bogolyubov transformation, the force takes the form of an off-shell in-medium two-body matrix in the superfluid phase multiplied by a BCS occupation number $2{\ensuremath{\rho}}_{m}$. This interaction is finite-ranged, nonlocal, total-momentum dependent, and density dependent. The factor $2{\ensuremath{\rho}}_{m}$ emerging from the recast of the gap equation provides a natural cutoff and makes zero-range approximations of the effective vertex meaningful. Performing such an approximation, the roles of the range and of the density dependence of the interaction can be disentangled. The isoscalar and isovector density dependences derived ab initio provide the pairing force with a strong predictive power when extrapolated toward the drip lines. Although finite ranged and nonlocal, the proposed interaction makes Hartree-Fock-Bogolyubov calculations of finite nuclei in coordinate space tractable. Through the two-basis method, its computational cost is of the same order as for a zero-range force.

Frequency and damping of hydrodynamic modes in a trapped Bose-condensed gas

Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive a variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable $^4$He is discussed. We also present calculations for the damping of the analogous $m=0$ monopole-quadrupole condensate mode in the superfluid phase.

Effective Lagrangians for scalar fields and finite size effects in field theory

We first discuss the approach of effective field theory in a d-dimensional Euclidean space. We consider a model with two interacting scalar fields (Lint(φ1,φ2)=(λ2/2)(φ1φ2)2) with masses m1 and m2. Assuming m2≫m1 we show that there is a decoupling in the effective theory describing the dynamic of the light mass field. Furthermore, we consider the presence of two parallel hyperplanes which break translational symmetry, with a natural cutoff satisfying m2≫Λ>m1. Then imposing Dirichlet and also Neumann boundary conditions, we study the perturbative renormalization of the effective theory (λφ4) in a region bounded by the two parallel hyperplanes in the one-loop approximation.

Future Galaxy Cluster Surveys: The Effect of Theory Uncertainty on Constraining Cosmological Parameters

Using the Fisher matrix formalism, we quantitatively investigate the constraints on a 10 dimensional space of cosmological parameters which may be obtained with future cluster surveys. We explore the dependence of the Omega_m constraint on both angular coverage and depth of field. We show that in each case there is a natural cutoff beyond which the constraints on Omega_m do not significantly improve. We also investigate the sensitivity of the constraints to changes in our knowledge of the Mass-Temperature (M-T) relation by including its normalization and scatter as two of the parameters in the Fisher matrix. To make our analysis more realistic, we have added, as priors, the Fisher matrices from hypothetical supernova and CMB experiments. We find that X-ray cluster surveys actually help to constrain the M-T relation, and explore the implications of this result.

Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random satisfiability problem, and its application to stop-and-restart resolutions.

A large deviation analysis of the solving complexity of random 3-satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that an exponentially small fraction of resolutions require a computation scaling linearly in the size of the instance only. This exponentially small probability of easy resolutions is analytically calculated, and the corresponding exponent is shown to be smaller (in absolute value) than the growth exponent of the typical resolution time. Our study therefore gives some theoretical basis to heuristic stop-and-restart solving procedures, and suggests a natural cutoff (the size of the instance) for the restart.

REFLECTIONS ON THE SPATIOTEMPORAL ASPECTS OF THE QUANTUM WORLD

The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold. The key to that problem is that the fuzziness of a variable can manifest itself only to the extent that less fuzzy variables exist. Inasmuch as there is nothing less fuzzy than the metric, this argues against a quantum-gravity phenomenology and suggests that a quantum theory of gravity is something of a contradiction in terms — a theory that would make it possible to investigate the physics on scales that do not exist, or to study the physical consequences of a fuzziness that has no physical consequences, other than providing a natural cutoff for the quantum field theories of particle physics.

Perturbation spectrum in inflation with a cutoff

It has been pointed out that the perturbation spectrum predicted by inflation may be sensitive to a natural ultraviolet cutoff, thus potentially providing an experimentally accessible window to aspects of Planck scale physics. A priori, a natural ultraviolet cutoff could take any form, but a fairly general classification of possible Planck scale cutoffs has been given. One of those categorized cutoffs, also appearing in various studies of quantum gravity and string theory, has recently been implemented into the standard inflationary scenario. Here, we continue this approach by investigating its effects on the predicted perturbation spectrum. We find that the size of the effect depends sensitively on the scale separation between cutoff and horizon during inflation.

New approach to Ginsparg-Wilson fermions

We expand the most general lattice Dirac operator D in a basis of simple operators. The Ginsparg-Wilson equation turns into a system of coupled quadratic equations for the expansion coefficients. Our expansion of D allows for a natural cutoff and the remaining quadratic equations can be solved numerically. The procedure allows us to find Dirac operators which obey the Ginpsparg-Wilson equation with arbitrary precision.

Quantization of Boson Fields in Quantum Geometry

It is shown that the introduction of an upper limit on the acceleration of particles provides a natural cutoff on momenta, avoiding the problem of ultraviolet divergencies in local quantum field theory. Such a cutoff turns out to be related to Planck energy.

Predictive Value of Quantitative PCR-Based Viral Burden Analysis for Eight Human Herpesviruses in Pediatric Solid Organ Transplant Patients

Human herpesviruses can cause significant morbidity and mortality in pediatric solid organ transplant recipients. It was hypothesized that viral burden quantification by polymerase chain reaction using an internal calibration standard could aid in distinguishing between viral disease and latency. Here we report the results of a 2-year prospective study of 27 pediatric solid organ (liver, kidney, or heart) transplant recipients in which multiple samples were analyzed for levels of all eight human herpesviruses by internal calibration standard-polymerase chain reaction. Herpes simplex viruses 1 and 2, varicella-zoster virus, and Kaposi's sarcoma-associated herpesvirus were not detected in any of these samples. Human herpesvirus types 6 and 7 were detected in half of the patients, but were present at low levels, similar to those found in reference populations. Epstein-Barr virus (EBV) and cytomegalovirus (CMV) were detected in 89% and 56% of the patients, respectively. Viral burden analysis suggested distinct patient populations for CMV, with a natural cutoff of 10,000 viral targets/ml blood strongly associated with disease. In some cases, a dramatic increase in CMV levels preceded clinical evidence of disease by several weeks. EBV viral burden was relatively high in the only patient presenting with an EBV syndrome. However, two other patients without evidence of EBV disease had single samples with high EBV burden. Rapid reduction in both EBV and CMV burden occurred with antiviral treatment. These data suggest that viral burden analysis using internal calibration standard-polymerase chain reaction for CMV, and possibly other herpesviruses, is an effective method for monitoring pediatric transplant patients for significant herpesvirus infection and response to therapy.

Significance of the Small and Medium Enterprises (SMEs) Sector in Pakistan and Assessment of its Employment Potential

Definitions and Sources Definitions: In this paper it is proposed to use the definition of selfemployed, small scale (2-9 employees), medium scale (10-99 employees) and large scale (100 employees and above) to discuss the issues relating to the Small and Medium Enterprise (SME) sector in Pakistan. The national pension (regulated through the Employees Old Age Benefit Institution Legislation) and health insurance (The Provincial Social Security Institutions Legislation) is applicable to institutions with 10 or more employees and provides a natural cut off point between the small scale and medium and large scale sectors. The cut off between the medium and large scale at 100 workers is also appropriate.