Compute Quantum Corrections Research Articles

EFFECTIVE EQUATIONS OF MOTION FOR QUANTUM SYSTEMS

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture are developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.

KK-masses in dipole deformed field theories

We reconsider aspects of non-commutative dipole deformations of field theories. Among our findings there are hints to new phases with spontaneous breaking of translation invariance (stripe phases), similar to what happens in Moyal-deformed field theories. Furthermore, using zeta-function regularization, we calculate quantum corrections to KK-state masses. The corrections coming from non-planar diagrams show interesting but non-universal behaviour. Depending on the type of interaction the corrections can make the KK-states very heavy but also very light or even tachyonic. Finally we point out that the dipole deformation of QED is not renormalizable!

Quantum deformations from toric geometry

We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and quantum deformations to the vacuum moduli space using Affleck-Dine-Seiberg superpotential arguments. Then we calculate the versal deformation to the corresponding toric geometry using a method due to Altmann, and show that the result is equivalent to the deformation calculated using gauge theory. In an appendix we will apply this technique to a few other examples. This is a new method for understanding the infrared dynamics of certain quiver gauge theories.

Quantum mechanics of the dynamic Kingdon trap

Classical mechanics is not sufficient to describe ion confinement in the dynamic Kingdon trap. We compute quantum corrections to the classical pseudopotential and supplement classical stability criteria with quantum stability criteria. Considering a realistic experimental scenario we show that it is possible to operate the dynamic Kingdon trap in the quantum regime.

A Physically Based Compact Gate<tex>$Chbox--V$</tex>Model for Ultrathin (EOT<tex>$sim1~hbox nm$</tex>and Below) Gate Dielectric MOS Devices

A computationally efficient and accurate physically based gate capacitance model of MOS devices with advanced ultrathin equivalent oxide thickness (EOT) oxides (down to 0.5 nm explicitly considered here) is introduced for the current and near future integrated circuit technology nodes. In such a thin gate dielectric regime, the modeling of quantum-mechanical (QM) effects simply with the assumption of an infinite triangular quantum well at the Si-dielectric interface can result in unacceptable underestimates of calculated gate capacitance. With the aid of self-consistent numerical Schro/spl uml/dinger-Poisson calculations, the QM effects have been reconsidered in this model. The 2/3 power law for the lowest quantized energy level versus field relations (E/sub 1//spl prop/F/sub ox//sup 2/3/), often used in compact models, was refined to 0.61 for electrons and 0.64 for holes, respectively, in the substrate in the regimes of moderate to strong inversion and accumulation to address primarily barrier penetration. The filling of excited states consistent with Fermi statistics has been addressed. The quantum-corrected gate capacitance-voltage (C-V) calculations have then been tied directly to the Fermi level shift as per the definition of voltage (rather than, for example, obtained indirectly through calculation of quantum corrections to the charge centroids offset from the interface). The model was implemented and tested by comparisons to both numerical calculations down to 0.5 nm, and to experimental data from n-MOS or p-MOS metal-gate devices with SiO/sub 2/, Si/sub 3/N/sub 4/ and high-/spl kappa/ (e.g., HfO/sub 2/) gate dielectrics on (100) Si with EOTs down to /spl sim/1.3 nm. The compact model has also been adapted to address interface states, and poly depletion and poly accumulation effects on gate capacitance.

Field theory approach to quantum interference in chaotic systems

We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading ('diagonal') contribution to the spectral form factor. Far-reaching structural parallels, as well as a number of differences, to recent semiclassical approaches to the problem are discussed.

Quantum inflaton, primordial perturbations, and CMB fluctuations

We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quantum analog of slow-roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant quantum effects into account. The results for the scalar, vector and tensor primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current Wilkinson Microwave Anisotropy Probe observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of (m{sup 2}/NH{sup 2}), where m is the inflaton mass and H the Hubble constantmore » at the moment of horizon crossing. An upper estimate turns to be about 4% for the cosmologically relevant scales. This quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it.« less

Quantum nonlinear spin switching model

We present a method, the dynamical cumulant expansion, that allows us to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum spin model $\ifmmode \hat{H}\else \^{H}\fi{}=\ensuremath{-}{H}_{z}{(t)S}_{z}+V(\mathbf{S})$ with ${H}_{z}(\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty})=\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ and $\ensuremath{\Psi}(\ensuremath{-}\ensuremath{\infty})=|\ensuremath{-}S〉$ to find $P(t)=(1\ensuremath{-}〈{S}_{z}{〉}_{t}/S)/2.$ The case $V(\mathbf{S})=\ensuremath{-}{H}_{x}{S}_{x}$ corresponds with the standard Landau-Zener-Stueckelberg model of tunneling at avoided level crossings for $N=2S$ independent particles mapped onto a single-spin-S problem, $P(t)$ being the staying probability. Here the solution does not depend on S and it follows, e.g., from the classical Landau-Lifshitz equation. A term $\ensuremath{-}{\mathrm{DS}}_{z}^{2}$ accounts for the particle interaction and it makes the model nonlinear and essentially quantum mechanical. The $1/S$ corrections obtained with our method are in good accord with a full quantum-mechanical solution if the classical motion is regular, as for $D>0.$ If the classical motion shows special points, as is the case for $D<0$ for particular values of the sweep rate, or is irregular (the biaxial-anisotropy model with field along the hard axis) the cumulant expansion fails.

Two-dimensional quantum-corrected black hole in a finite size cavity

We consider the gravitation-dilaton theory (not necessarily exactly solvable), whose potentials represent a generic linear combination of an exponential and linear functions of the dilaton. A black hole, arising in such theories, is supposed to be enclosed in a cavity, where it attains thermal equilibrium, whereas outside the cavity the field is in the Boulware state. We calculate quantum corrections to the Hawking temperature $T_{H}$, with the contribution from the boundary taken into account. Vacuum polarization outside the shell tend to cool the system. We find that, for the shell to be in the thermal equilibrium, it cannot be placed too close to the horizon. The quantum corrections to the mass due to vacuum polarization vanish in spite of non-zero quantum stresses. We discuss also the canonical boundary conditions and show that accounting for the finiteness of the system plays a crucial role in some theories (e.g., CGHS), where it enables to define the stable canonical ensemble, whereas consideration in an infinite space would predict instability.

Long time evolution of quantum averages near stationary points

We construct explicit expressions for quantum averages in coherent states for a Hamiltonian of degree 4 with a hyperbolic stagnation point. These expressions are valid for all times and “collapse” (i.e., become infinite) along a discrete sequence of times. We compute quantum corrections compared to classical expressions. These corrections become significant over a time period of order C log 1 ℏ .

Quantum corrections to the mass of the supersymmetric vortex

We calculate quantum corrections to the mass of the vortex in N=2 supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a box and apply the zeta function regularization. The boundary conditions inevitably violate a part of the supersymmetries. Remaining supersymmetry is however enough to ensure isospectrality of relevant operators in bosonic and fermionic sectors. A non-zero correction to the mass of the vortex comes from finite renormalization of couplings.

Unrenormalizable theories can be predictive

Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of a maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enables us to make unique predictions in the infrared regime in terms of a finite number of independent parameters. Therefore, this method might provide a way for calculating quantum corrections in a low-energy effective theory of quantum gravity.

Non-Perturbative Renormalization Group Analysis in Quantum Mechanics

We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start with anharmonic oscillators and proceed to asymmetric double well potentials, supersymmetric quantum mechanics and many particle systems.

Discrete symmetries of the superpotential and calculation of disk invariants

The integrality of Ooguri-Vafa disk invariants is verified using discrete symmetries of the superpotential of the mirror Landau-Ginzburg theory to calculate quantum corrections to the boundary variables. We show that these quantum corrections are completely determined if we assume that the discrete symmetry of the superpotential also holds in terms of the quantum corrected variables. We discuss the case of local P^2 blown up at three points and local F_2 blown up at two points in detail.

Ultraviolet behavior of bosonic quantum membranes

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $\beta = 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.

Method for Direct Measurement of the Wigner Function in Cavity QED and Ion Traps

Phase space representations are very useful in quantum mechanics since they allow the calculation of correlation functions of operators as classical-like integrals, and are also helpful for the study of the transition to classical physics. The oldest of such representations is due to Wigner [1], who used it as a convenient tool to calculate quantum corrections to classical statistical mechanics. It was shown by Moyal [2] that the quantum average of a Weyl-ordered (symmetric-ordered) function of the momentum and position operators could be expressed as a classical-like average of the corresponding classical function (in which the operators are replaced by c numbers), with the Wigner distribution acting as a weight measure in phase space [3]. The uncertainty principle forbids, however, the interpretation of this function as a probability distribution, since it is not possible to determine simultaneously the momentum and the position of a particle. In fact, it is easy to find examples of states for which the Wigner distribution assumes negative values. This fact may lead to the idea that it does not correspond to any directly measured quantity. Up until now, this notion has been upheld by the fact that the different schemes proposed so far to determine the Wigner distribution of a quantum system rely either on tomographic reconstructions from data obtained in homodyne measurements [4,5] or on convolutions obtained by photon counting [6]. It is the purpose of this Letter to show that the Wigner function can be directly measured, through a very simple scheme, especially suitable to experiments in cavity quantum electrodynamics and in ion traps. This is especially important in view of recent experimental results concerning the production and detection of coherent superpositions of localized mesoscopic states [7,8]. In these experiments, the existence of coherence is inferred from partial information obtained about the system. A method yielding more complete knowledge onf the quantum states involved would be highly desirable. Quantum tomography schemes for determining the vibrational state of a trapped ion were proposed in [5]. In cavity QED, information on the field must be obtained from probe atoms, since the high Q of the cavity and the weak intensities involved do not allow the direct measurement of the field. A method for realizing the “quantum endoscopy” of a field in a cav-

Classical real time correlation functions and quantum corrections at finite temperature

We consider quantum corrections to classical real time correlation functions at finite temperature. We derive a semi-classical expansion in powers of h with coefficients including all orders in the coupling constant. We give explicit expressions up to order h 2 We restrict ourselves to a scalar theory. This method, if extended to gauge theories, might be used to compute quantum corrections to the high temperature baryon number violation rate in the Standard Model.

Unitary theory of evaporating two-dimensional black holes

We study a manifestly unitary formulation of two-dimensional dilaton quantum gravity based on the reduced phase space quantization. The spacetime metric operator can be expanded in a formal power series of the matter energy - momentum tensor operator. This expansion can be used for calculating quantum corrections to the classical black hole metric. This is done by evaluating the expectation value of the metric operator in an appropriate class of the physical states. When the normal ordering in the metric operator is chosen to be with respect to Kruskal vacuum, the lowest-order semiclassical metric is exactly the one-loop effective action metric discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry describes an evaporating black hole which ends up as a remnant. The calculation of higher-order corrections and implications for the black hole fate are discussed.

Toda soliton mass corrections and the particle-soliton duality conjecture

We compute quantum corrections to soliton masses in affine Toda theories with imaginary exponentials based on the nonsimply-laced Lie algebras c n (1) We find that the soliton mass ratios renormalize nontrivially, in the same manner as those of the fundamental particles of the theories with real exponentials based on the nonsimply-laced algebras b n (1) This gives evidence that the conjectured relation between solitons in one Toda theory and fundamental particles in a dual Toda theory holds also at the quantum level. This duality can be seen as a toy model for S-duality.

Kinetic energies of liquid and solid neon.

We have calculated the kinetic energies of liquid and solid neon in the temperature range 9.2--35 K. We have used the Wigner-Kirkwood expansion technique for the calculation of quantum corrections to the kinetic energy up to the order of ${\mathrm{\ensuremath{\Elzxh}}}^{6}$ in the expansion. All the averages are calculated by molecular dynamics computer simulation. Our results are in agreement with the experimental findings of Peek et al. Both the Lennard-Jones and Aziz pair potentials have been used in calculations with comparable results.