Large Field Region Research Articles

Searching strong ‘spin’-orbit coupled one-dimensional hole gas in strong magnetic fields

We show that a strong ‘spin’-orbit coupled one-dimensional hole gas is achievable via applying a strong magnetic field to the original two-fold degenerate (spin degeneracy) hole gas confined in a cylindrical Ge nanowire. Both strong longitudinal and strong transverse magnetic fields are feasible to achieve this goal. Based on quasi-degenerate perturbation calculations, we show the induced low-energy subband dispersion of the hole gas can be written as , a form exactly the same as that of the electron gas in the conduction band. Here the Pauli matrices σ z,x represent a pseudo spin (or ‘spin’), because the real spin degree of freedom has been split off from the subband dispersions by the strong magnetic field. Also, for a moderate nanowire radius R = 10 nm, the induced effective hole mass and the ‘spin’-orbit coupling α (0.35 ∼ 0.8 eV Å) have a small magnetic field dependence in the studied magnetic field interval 1 < B < 15 T, while the effective g-factor of the hole ‘spin’ only has a small magnetic field dependence in the large field region.

Eternal Higgs inflation and the cosmological constant problem

We investigate the Higgs potential beyond the Planck scale in the superstring theory, under the assumption that the supersymmetry is broken at the string scale. We identify the Higgs field as a massless state of the string, which is indicated by the fact that the bare Higgs mass can be zero around the string scale. We find that, in the large field region, the Higgs potential is connected to a runaway vacuum with vanishing energy, which corresponds to opening up an extra dimension. We verify that such universal behavior indeed follows from the toroidal compactification of the non-supersymmetric $SO(16)\times SO(16)$ heterotic string theory. We show that this behavior fits in the picture that the Higgs field is the source of the eternal inflation. The observed small value of the cosmological constant of our universe may be understood as the degeneracy with this runaway vacuum, which has vanishing energy, as is suggested by the multiple point criticality principle.

Cooper pairsʼ magnetic moment in MCFL color superconductivity

We investigate the effect of the alignment of the magnetic moments of Cooper pairs of charged quarks that form at high density in three-flavor quark matter. The high-density phase of this matter in the presence of a magnetic field is known to be the Magnetic Color–Flavor-Locked (MCFL) phase of color superconductivity. We derive the Fierz identities of the theory and show how the explicit breaking of the rotational symmetry by the uniform magnetic field opens new channels of interactions and allows the formation of a new diquark condensate. The new order parameter is a spin-1 condensate proportional to the component in the field direction of the average magnetic moment of the pairs of charged quarks. The magnitude of the spin-1 condensate becomes comparable to the larger of the two scalar gaps in the region of large fields. The existence of the spin-1 condensate is unavoidable, as in the presence of a magnetic field there is no solution of the gap equations with nonzero scalar gaps and zero magnetic moment condensate. This is consistent with the fact that the extra condensate does not break any symmetry that has not already been broken by the known MCFL gaps. The spin-1 condensate enhances the condensation energy of pairs formed by charged quarks and the magnetization of the system. We discuss the possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density.

Nonminimally coupled hybrid inflation

We discuss the hybrid inflation model where the inflaton field is nonminimally coupled to gravity. In the Jordan frame, the potential contains $\phi^4$ term as well as terms in the original hybrid inflation model. In our model, inflation can be classified into the type (I) and the type (II). In the type (I), inflation is terminated by the tachyonic instability of the waterfall field, while in the type (II) by the violation of slow-roll conditions. In our model, the reheating takes place only at the true minimum and even in the case (II) finally the tachyonic instability occurs after the termination of inflation. For a negative nonminimal coupling, inflation takes place in the vacuum-dominated region, in the large field region, or near the local minimum/maximum. Inflation in the vacuum dominated region becomes either the type (I) or (II), resulting in blue or red spectrum of the curvature perturbations, respectively. Inflation around the local maximum can be either the type (I) or the type (II), which results in the red spectrum of the curvature perturbations, while it around the local minimum must be the type (I), which results in the blue spectrum. In the large field region, to terminate inflation, potential in the Einstein frame must be positively tilted, always resulting in the red spectrum. We then numerically solve the equations of motion to investigate the whole dynamics of inflaton and confirm that the spectrum of curvature perturbations changes from red to blue ones as scales become smaller.

A phase transition between small- and large-field models of inflation

We show that models of inflection point inflation exhibit a phase transition from a region in parameter space where they are of large-field type to a region where they are of small-field type. The phase transition is between a universal behavior, with respect to the initial condition, at the large-field region and non-universal behavior at the small-field region. The order parameter is the number of e-foldings. We find integer critical exponents at the transition between the two phases.

On the Kertész line: Some rigorous bounds

We study the Kertész line of the q-state Potts model at (inverse) temperature β in the presence of an external magnetic field h. This line separates the two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin–Kasteleyn representation of the model. It is known that the Kertész line hK(β) coincides with the line of first order phase transition for small fields when q is large enough. Here, we prove that the first order phase transition implies a jump in the density of the infinite cluster; hence, the Kertész line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that hK(β) equals log(q−1)−log(β−βp) to the leading order, as β goes to βp=−log(1−pc), where pc is the threshold for bond percolation.

Direct observation of large, quasi‐static, parallel electric fields in the auroral acceleration region

The three‐axis electric field experiment on the Polar satellite provides direct observations of electric field components parallel and perpendicular to the local magnetic field with no arbitrary adjustment parameters. Approximately 750 perigee passes through each of the two southern auroral zones at a geocentric altitude of about two Earth radii have been computer‐searched for parallel electric fields whose eight point (0.2 or 0.4 second) average exceeded 100 mV/m. After elimination of spurious events due to shadowing, saturation, and ten other effects, four events containing parallel fields of 200–300 mV/m, remain. These four events all occur in upward field aligned current regions, their parallel electric fields are all positive such that . &gt;0, and they occur at boundaries between regions of active and quiet perpendicular electric fields. Up‐going ion beams are observed in the active field regions, and the plasma density is higher in the quiet field regions than in the adjacent active field regions. These boundaries are interpreted in terms of model equipotentials, some of which are below the spacecraft in the large field regions and all of which are above the spacecraft in the quiet field regions. In this model, the expected location of large parallel electric fields is where they are observed. That the potential difference measured by the electric field instrument along the vehicle trajectory and the kinetic energy of the up‐going ions are equal lends further credence to the data and its interpretation.

Large field renormalization. I. The basic step of the ? operation

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by ℝ, removes the main obstacle to prove the ultraviolet stability of four-dimensional gauge field theories. The proof will be completed in the second part of this paper.

A phase cell approach to Yang-Mills theory

In this paper the basic local stability result is obtained, in a form valid in both small field and large field regions. To achieve this, some modifications are made in both the action and the renormalization group transformation. Though there is some sacrifice of elegance in these modifications, the establishment of this local stability estimate yields the most basic ingredient of the phase cell cluster expansion, good estimates for all the actions.Incidental to the estimates of this paper we establish some results on “lattice geometry,” interesting in their own right. A bound on the “minimum area” of a loop of lengthl, ind dimensions, is obtained asl 2/8(1−1/d). This, a best possible bound, was obtained for us by A. Blass. We also construct a “radial” maximal tree for the lattice ind dimensions. We hope to stimulate someone to find a better construction of “radial” trees.

A non-Gaussian renormalization group fixed point for hierarchical scalar lattice field theories

A rigorous method is developed to handle the “large field problems” in the Wilson-Kadanoff renormalization group approach to critical lattice systems of unbounded spins. We use this method to study in a hierarchical approximation the non-Gaussian renormalization group fixed point which governs the infrared behaviour of critical lattice field theories in three dimensions. The method is an improvement of the analyticity techniques of Gawedzki and Kupiainen: using Borel summation techniques we are able to incorporate the “large field region” into the “perturbative region” so that the theory is completely described in terms of convergent expansions.

Is our vacuum metastable?

In spontaneously broken gauge theories of particle interactions there are sometimes several local minima of the effective potential. Any of these minima can serve as a vacuum in the sense that we can expand the fields around their values at the minimum, interpret the quantized fluctuations around the minimum as particles, and compare the properties of these particles with experiment. One might think that only the state with absolutely minimum energy could be what we ordinarily call our vacuum, as the other local minima will inevitably decay into this lowest one. However, this is not necessarily the case, because it is possible for the lifetime of a metastable vacuum to be very long, even when compared with the age of the Universe. Furthermore, the energy densities available in present laboratory or astrophysical environments are much less than the barriers which exist in field space between the different local minima, and so we have no direct sensitivity to the presence of a possibly lower vacuum state. (A possible exception to this are magnetic monopoles which do probe the large field region.) If it is not the absolute minimization of the effective potential, what does determine the present vacuum state of the Universe? We argue here that it is determined cosmologically by the dynamical evolution of the Universe from the hot, dense phase which existed shortly after the big bang to the present1,2.

Comparison and Discussion of Some Periodic Domain Structures

The energy density of seven periodic domain structures in sheets of uniaxial magnetic materials placed in a magnetic field Hz perpendicular to the sheet is calculated.1 The following periodic structures are considered: I. A hexagonal bubble lattice; within the cylinders the magnetization Ms is reversed with respect to Hz. II. The negative of I; within the cylinders, Ms and Hz have the same directions. III. A similar but square lattice of bubbles and its ``negative'' (IV). V. A honeycomb structure where the prisms are the reversed domains. VI. The negative of V. VII. A strip lattice. The energy density is minimized with respect to two variables. Comparing the structures I-VII it is found that: (1) In a large field region a hexagonal bubble lattice (I) has the lowest energy. At low fields, VII has the lowest energy. (2) The structures where the reversed domains are connected with each other (II, IV, VI) have a higher energy than their negatives (I, III, V). (3) The radius of a bubble in a hexagonal lattice (I) differs at the same magnetic field considerably from the radius of an isolated bubble. (4) The energy of the honeycomb structure V is always higher than the energy of structure I. Comparing VI and II this is not the case: at higher field, structure VI has a lower energy than structure II. (5) Comparing the fields at which for I, III, V, and VII the lattice distance becomes infinite, we found the lowest field for VII and the highest for I and III. The occurrence of the different structures will of course not only be determined by the energy difference between them but also by the number of nucleation points and the possible energy barriers. The occurrence of I in zero field seems to be possible since the lattice distance for I is almost the same at zero field as at the lowest field for which I have the lowest energy. If I can occur at low fields the same holds for II, since it can be formed from I by reversing Hz. For higher fields, II will go over into VI. At a field where the lattice distance of VI becomes infinite, an isolated interconnected reversed domain will appear. This can be a hollow cylindrical domain. Changing the field in such a way that the well-known transitions occur: ring→bubble→strip→strip lattice, a transition from I→VII via different structures has been described above. Such a transition was also found experimentally. Detailed calculations will be published elsewhere.1