Order Quantum Corrections Research Articles

Quantum corrections to dilute Bose liquids

It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002)) that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons (boselets), fermions (fermilets) and their mixtures (ferbolets) by controlling their interaction properties by the means of a Feshbach resonance. We extend the previous mean--field analysis of these quantum liquids by computing the lowest order quantum corrections to the ground state energy and the depletion of the Bose--Einstein condensate and by estimating higher order corrections as well. We show that the quantum corrections are relatively small and controlled by the diluteness parameter $\sqrt{n|a|^3} \ll 1$, even though strictly speaking in this case there is no low density expansion.

The Use of Quantum Potentials for Confinement and Tunnelling in Semiconductor Devices

As MOSFETs are scaled to sub 100 nm dimensions, quantum mechanical confinement in the direction normal to the silicon dioxide interface and tunnelling (through the gate oxide, band-to-band and from source-to-drain) start to strongly affect their characteristics. Recently it has been demonstrated that first order quantum corrections can be successfully introduced in self-consistent drift diffusion-type models using Quantum Potentials. In this paper we describe the introduction of such quantum corrections within a full 3D drift diffusion simulation framework. We compare the two most popular quantum potential techniques: density gradient and the effective potential approaches, in terms of their justification, accuracy and computational efficiency. The usefulness of their 3D implementation is demonstrated with examples of statistical simulations of intrinsic fluctuation effects in decanano MOSFETs introduced by discrete random dopants. We also discuss the capability of the density gradient formalism to handle direct source-to-drain tunnelling in sub 10 nm double-gate MOSFETS, illustrated in comparison with Non-Equilibrium Green's Functions simulations.

SECOND ORDER QUANTUM CORRECTIONS TO THE CLASSICAL REFLECTION FACTOR OF THE SINH–GORDON MODEL

The sinh–Gordon model on a half-line with integrable boundary conditions is considered in low order perturbation theory developed in affine Toda field theory. The quantum corrections to the classical reflection factor of the model are studied up to the second order in the difference of the two boundary parameters and to one loop order in the bulk coupling. It is noticed that the general form of the second order quantum corrections are consistent with Ghoshal's formula.

Quantized bulk fermions in the Randall-Sundrum brane model

The lowest order quantum corrections to the effective action arising from quantized massive fermion fields in the Randall-Sundrum background spacetime are computed. The boundary conditions and their relation with gauge invariance are examined in detail. The possibility of Wilson loop symmetry breaking in brane models is also analyzed. The self-consistency requirements, previously considered in the case of a quantized bulk scalar field, are extended to include the contribution from massive fermions. It is shown that in this case it is possible to stabilize the radius of the extra dimensions but it is not possible to simultaneously solve the hierarchy problem, unless the brane tensions are dramatically fine-tuned, supporting previous claims.

Quantized bulk scalar fields in the Randall–Sundrum brane model

We examine the lowest order quantum corrections to the effective action arising from a quantized real scalar field in the Randall–Sundrum background spacetime. The leading term is the familiar vacuum, or Casimir, energy density. The next term represents an induced gravity term that can renormalize the 4-dimensional Newtonian gravitational constant. The calculations are performed for an arbitrary spacetime dimension. Two inequivalent boundary conditions, corresponding to twisted and untwisted field configurations, are considered. A careful discussion of the regularization and renormalization of the effective action is given, with the relevant counterterms found. It is shown that the requirement of self-consistency of the Randall–Sundrum solution is not simply a matter of minimizing the Casimir energy density. The massless, conformally coupled scalar field results are obtained as a special limiting case of our results. We clarify a number of differences with previous work.

Quantum partition functions from classical distributions: Application to rare-gas clusters

We investigate the thermodynamic behavior of quantum many-body systems using several methods based on classical calculations. These approaches are compared for the melting of Lennard-Jones (LJ) clusters, where path-integral Monte Carlo (PIMC) results are also available. First, we examine two quasiclassical approaches where the classical potential is replaced by effective potentials accounting for quantum corrections of low order in ℏ. Of the Wigner–Kirkwood and Feynman–Hibbs effective potentials, only the latter is found to be in quantitative agreement with quantum simulations. However, both potentials fail to describe even qualitatively the low-temperature regime, where quantum effects are strong. Our second approach is based on the harmonic superposition approximation, but with explicit quantum oscillators. In its basic form, this approach is in good qualitative agreement with PIMC results, and becomes more accurate at low temperatures. By including anharmonic corrections in the form of temperature-dependent frequency shifts, the agreement between the quantum superposition and the PIMC results becomes quantitative for the caloric curve of neon clusters. The superposition method is then applied to larger clusters to study the influence of quantum delocalization on the melting and premelting of LJ19, LJ31, LJ38, and LJ55. The quantum character strongly affects the thermodynamics via changes in the ground state structure due to increasing zero-point energies. Finally, we focus on the lowest temperature range, and we estimate the Debye temperatures of argon clusters and their size variation. A strong sensitivity to the cluster structure is found, especially when many surface atoms reorganize as in the anti-Mackay/Mackay transition. In the large size regime, the Debye temperature smoothly rises to its bulk limit, but still depends slightly on the growth sequence considered.

MATAD: a program package for the computation of MAssive TADpoles

In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta. In this paper a program package is described which can deal with one-, two-, and three-loop vacuum integrals with one non-zero mass parameter. The principle structure is introduced and the main parts of the package are described in detail. Explicit examples demonstrate the fields of application.

Quantum corrections to the energy density of a homogeneous Bose gas

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of $\sqrt {\rho a^3 }$ , where ρ is the number density and a is the S-wave scattering length. We calculate the ground state energy density to second order in $\sqrt {\rho a^3 }$ . The coefficient of the ρa 3correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on a, but also on an extra parameter that describes the low energy 3 → 3 scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is ρal V 2 , and l V is the length scale set by the van der Waals potential.

Magnetization curve of a square-lattice Heisenberg antiferromagnet

We calculate the uniform magnetization of a spin-1/2 Heisenberg square lattice antiferromagnet at $T=0$ in magnetic fields up to the saturation field in the framework of spin-wave theory including quantum corrections of the second order in $1/S$. External field generally suppresses zero-point fluctuations, which leads to an upward curvature of the magnetization curve at low fields and logarithmic singularity close to the saturation.

SU(5) monopoles and the dual standard model

We find the spectrum of magnetic monopoles produced in the symmetry breaking SU(5) to [SU(3)\times SU(2)\times U(1)']/Z_6 by constructing classical bound states of the fundamental monopoles. The spectrum of monopoles is found to correspond to the spectrum of one family of standard model fermions and hence, is a starting point for constructing the dual standard model. At this level, however, there is an extra monopole state - the ``diquark'' monopole - with no corresponding standard model fermion. If the SU(3) factor now breaks down to Z_3, the monopoles with non-trivial SU(3) charge get confined by strings in SU(3) singlets. Another outcome of this symmetry breaking is that the diquark monopole becomes unstable (metastable) to fragmentation into fundamental monopoles and the one-one correspondence with the standard model fermions is restored. We discuss the fate of the monopoles if the [SU(2)\times U(1)']/Z_2 factor breaks down to U(1)_Q by a Higgs mechanism as in the electroweak model. Here we find that monopoles that are misaligned with the vacuum get connected by strings even though the electroweak symmetry breaking does not admit topological strings. We discuss the lowest order quantum corrections to the mass spectrum of monopoles.

Non-Critical Open Strings Beyond the Semiclassical Approximation

We studied the lowest order quantum corrections to the macroscopic wave functions Γ(A,ℓ) of non-critical string theory using the semiclassical expansion of Liouville theory. By carefully taking the perimeter constraint into account we obtained a new type of boundary condition for the Liouville field which is compatible with the reparametrization invariance of the boundary and which is not only a mixture of Dirichlet and Neumann types but also involves an integral of an exponential of the Liouville field along the boundary. This condition contains an unknown function of A/ℓ2. We determined this function by computing part of the one-loop corrections to Γ(A,ℓ).

Nontrivial classical backgrounds with vanishing quantum corrections

Vacuum polarization and particle production effects in classical electromagnetic and gravitational backgrounds can be studied by the effective lagrangian method. Background field configurations for which the effective lagrangian is zero are special in the sense that the lowest order quantum corrections vanishes for such configurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical field configurations for which all the scalar invariants are zero. We verify this conjecture, by explicitly evaluating the effective lagrangian, for non-trivial electromagnetic and gravitational backgrounds with vanishing scalar invariants. The implications of this result are discussed.

Gravitational scattering of quantum fields and spacetime geometry

We compute the lowest order quantum correction to the elastic scattering cross section for a massive spin-0 particle interacting with an external gravitational field. The result shows that quantum effects induce a breakdown of the geometrical picture afforded by the classical principle of equivalence.

Cosmological structure problem of the pre-big bang scenario

We calculate the density and gravitational wave spectrums generated in a version of string cosmology termed pre-big bang scenario. The large scale structures are originated from quantum fluctuations of the metric and dilaton field during a pole-like inflation stage driven by a potential-less dilaton field realized in the low-energy effective action of string theory. The generated classical density field and the gravitational wave in the second horizon crossing epoch show tilted spectrums with n ⋍ 4 and n T ⋍ 3 , respectively. These differ from the observed spectrum of the large angular scale anisotropy of the cosmic microwave background radiation which supports scale invariant ones with n ⋍ 1 and n T ⋍ 0 . This suggests that the pre-big bang stage is not suitable for generating the present day observable large scale structures, and suggests the importance of investigating the quantum generation processes during stringy era with higher order quantum correction terms.

Three-dimensional ordering in bct antiferromagnets due to quantum disorder.

Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearestneighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting (in a mean-field sense) antiferromagnetic planes which together form a body-centeredtetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order J2⊥/(J2S), where J, the antiferromagnetic in-plane exchange interaction, is assumed to dominate J⊥, the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign σi (i=1,2,...M) to the staggered moment of the planes. Our result for the zero-point energy (for M>2) up to the sixth order in j=J⊥/J is E({σi}) =E1+CEG(j6/S)[-2σ1σ3-2σM−2σM+2∑i =1M-2σiσi+2-3∑i=1M-3σiσi+1σi+2σi+3], where C>0 and E1 are constants independent of the σ’s, and EG is the classical ground-state energy. (Here sums from i to j when j 4 second-neighboring planes are antiferromagnetically coupled in the ground state and thus the three-dimensional spin structure cannot be described by a single wave vector, as is often assumed. At order j4, σ-dependent terms first appear at order 1/S3 and these also favor antiferromagnetic coupling of alternate planes. Disciplines Physics | Quantum Physics Comments At the time of publication, author A. Brooks Harris was also affiliated with Oxford University and Tel Aviv University. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/345 Three-dimensional ordering in bct antiferromagnets due to quantum disorder T. Yildirim University of Maryland, College Park, Maryland 20742; National Institute of Standards and Technology, Gaithersburg, Maryland 20899; and Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104 A. B. Harris Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104; Theoretical Physics, Oxford University, Oxford, OX2 3NP, United Kingdom; and School of Physics and Astronomy, Raymond and Beverly Sackler Institute of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel E. F. Shender Department of Physics, University of California, Berkeley, California 94720 and Institute of Nuclear Physics, St. Petersburg, Russia ~Received 11 August 1995! Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearestneighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting ~in a mean-field sense! antiferromagnetic planes which together form a body-centered-tetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order J' 2 /(JS), where J , the antiferromagnetic in-plane exchange interaction, is assumed to dominate J' , the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign s i (i51,2, . . . M ) to the staggered moment of the planes. Our result for the zero-point energy ~for M.2! up to the sixth order in j5J' /J is E~$si%!5E11CEG~j 6/S!F22s1s322sM22sM12( i51 M22 sisi1223( i51 M23 sisi11si12si13G, where C.0 and E1 are constants independent of the s’s, and EG is the classical ground-state energy. ~Here sums from i to j when j,i are interpreted to be zero.! Surprisingly, there is no s-dependent contribution at order j/S . This result shows that for M.4 second-neighboring planes are antiferromagnetically coupled in the ground state and thus the three-dimensional spin structure cannot be described by a single wave vector, as is often assumed. At order j, s-dependent terms first appear at order 1/S and these also favor antiferromagnetic coupling of alternate planes.

New asymptotic expansion method for the Wheeler-DeWitt equation.

A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"{o}dinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of $m_p^2$ approaching infinity. The higher order quantum corrections of the gravity to the matter field are found. The new asymptotic expansion method is valid throughout all regions of superspace compared with other expansion methods with a certain limited region of validity. We apply the new asymptotic expansion method to the minimal FRW universe.

Quantum mass corrections for [formula omitted] affine Toda field theory solitons

We calculate the quantum corrections to the masses of the solitons in the imaginary coupling constant C 2 (1) affine Toda field theory. There are essentially two different species of solitons and classically the ratio of their masses is independent of the coupling constant. Unlike the case of A n (1) investigated by Hollowood in which the soliton mass ratios are unaltered by the leading order quantum corrections, we find that the quantum corrections introduce a dependence on the coupling constant to the ratio of the masses of the two solitons in the C 2 (1) theory. As has been known for some time, the ratio of the particle masses is also changed to one loop, and the classical relation between soliton and particle masses found by Olive et al. is preserved.

THEORY OF SPONTANEOUS RADIATION BY BOSONS IN QUASI-CLASSICAL TRAJECTORY-COHERENT APPROXIMATION

The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.

Canonical number projection in a simple nuclear model.

The heat capacity for a system of nucleons as a function of temperature is determined from the canonical partition function, which is projected from an approximation to the grand canonical partition function. This approximation is obtained from a functional integral representation of the partition function, including both thermodynamic fluctuations and first order quantum corrections. The number projection methods include a simple contour integration of Wick rotation'', and a Chebyschev polynomial expansion, both of which are formally exact. The above procedure is tested in a simple [ital i][sub 13/2] pairing model for which the exact canonical and grand canonical results can be obtained. It is found that both number projection methods fail to predict the position or the height of the peak in the heat capacity due to errors in the approximation to the grand partition function, even though the path integral approximation is very good.

One-loop effects of non-standard triple gauge boson vertices

Low energy effects of generic extensions of the Standard Model can be comprehensively parametrized in terms of higher dimensional effective operators. After the success of all the recent precision tests on the Standard Model, we argue that any sensible description of these extensions at the Z-scale must be stable under higher order quantum corrections. The imposition of SU(2) L×U(1) Y gauge invariance seems to be the simplest and most natural way to fulfill this requirement. With this assumption all the possible deviations from the standard triple gauge boson vertices can be consistently parametrized in terms of a finite set of gauge invariant operators. We deal here with those operators that do not give any tree level effect on present experimental observables and constrain them by computing their effects at the one-loop level. We conclude that for a light Higgs boson, the direct measurement at LEP200 can improve present bounds on these “blind directions”, while for a heavy Higgs it is most unlikely to provide any new information.