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Pervez Hoodbhoy

Publications and source records attributed to Pervez Hoodbhoy.

At least 19 recordsLinked to original sources
arXiv2026

Exact Semiclassical Dynamics in a Multidimensional Quartic Potential: Multi-Flavor Instantons and Pre-Factor Dominance at Strong Coupling

We present an exact semi-classical analysis of a coupled multi-degree-of-freedom quantum system governed by a symmetric quartic potential with four degenerate minima. Starting from the Euclidean path integral, we identify distinct paths that are longitudinal, transverse, and diagonal, each corresponding to distinct instanton configurations that mediate tunneling between vacua. The continuous translational zero mode for each coupled trajectory is extracted rigorously by transforming the fluctuation operator into a comoving rotating frame, explicitly incorporating curvature-induced fictitious forces. By evaluating the exact functional determinants via the Gelfand-Yaglom method and mapping the multi-flavor dilute instanton gas onto a weighted $K_4$ adjacency matrix, we analytically derive the transition amplitudes and ground-state energy splittings. Crucially, our exact continuum treatment reveals that for strong coupling, the usual exponential can be overpowered in certain parameter ranges by the "pre-factor". This quantity, which arises from quadratic level fluctuations in the direction transverse to the free direction, turns out to have an essential singularity that would be hard to spot in standard discretized instanton approximations.

quant-ph↗
arXiv2026

Coupled Instantons In A Four-Well Potential With Application To The Tunneling Of A Composite Particle

Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is examined in detail. It has three instanton types or flavors with distinct actions. For weak coupling and subject to there being a single large (or small) parameter, the interactive system can be handled perturbatively. The zero mode problem arising from time translation symmetry is handled via the Fadeev-Popov procedure. A diagrammatic procedure allows corrections to the fluctuation determinant to be calculated systematically. Independent instanton contributions are summed over by extending the dilute gas approximation to three flavors and energy splittings of the lowest four states is calculated. All tunneling amplitudes are concisely expressed in terms of elementary functions. While the model is possibly useful for a variety of physical systems, an application is made here to the tunneling of a composite particle in one dimension.

quant-ph↗
arXiv2020

Instability induced by exchange forces in a 2-D electron gas in a magnetic field with uniform gradient

The exchange interaction is investigated theoretically for electrons confined to a 2-D sample placed in a linearly varying magnetic field perpendicular to the plane. Unusual and interesting behavior is predicted: starting from zero, as one adds electrons to the system, its size will increase continuously but will then collapse. However this collapse will be reversed as the number crosses another critical value, which we estimate here. For electron parameters typical for 2DEG's, the instability could be observable at sufficiently low electron densities. A Hartree Fock equation is derived and investigated. We also show that in an appropriate asymptotic limit an approximate local potential can be derived. One key lesson is that the exchange interaction is large and cannot be reasonably excluded from any valid theoretical investigation.

cond-mat.str-el↗
arXiv2018

Augmenting the Gauge-Gravity Correspondence to include Hadron Polarizabilities

ADS/CFT models have achieved considerable success in describing hadronic properties such as masses and Regge trajectories. Even if the minimal vertex that couples photons to structureless spin-zero fields is used, one still ends up with electromagnetic form factors of hadrons that are in fair to good agreement with experiment. However, contradicting both experiment and intuition, this minimal model gives zero for hadronic electric and magnetic polarizabilities. We show here that if effective vertices are used, and axial and vector mesons are allowed to propagate as intermediate states, then the static polarizabilities can in principle be computed from ADS/CFT.

hep-ph↗
arXiv2018

Quantum Tunneling Of Electron Snake States In An Inhomogeneous Magnetic Field

In a two dimensional free electron gas (2DEG) subjected to a perpendicular spatially varying magnetic field, the classical paths of electrons are snake-like trajectories that weave along the line where the field crosses zero. But quantum mechanically this system is described by a symmetric double well potential which, for low excitations, leads to very different electron behavior. We compute the spectrum, as well as the wavefunctions, for states of definite parity in the limit of nearly degenerate states, i.e. for electrons sufficiently far from the $B_z=0$ line. Transitions between the states are shown to give rise to a tunneling current. If the well is made asymmetrical by a time-dependent parity breaking perturbation then Rabi-like oscillations between parity states occur. Resonances can be excited and used to stimulate the transfer of electrons from one side of the potential barrier to the other through quantum tunneling.

cond-mat.mes-hall↗
arXiv2008

ADS/CFT Applied To Vector Meson Emission From A Heavy Accelerated Nucleus

We consider a classical source, moving on the 4-D boundary of a 5-D ADS space, that is coupled to quantum fields residing in the bulk. Bremsstrahlung-like radiation of the corresponding quanta is shown to occur and the S-matrix is derived assuming that the source is sufficiently massive so that recoil effects are negligible. As an illustrative example, using the ADS hard-wall model, we consider vector mesons coupled to a heavy nucleus that is moved around at high speed in an accelerator ring. The meson radiation rate is found to be finite but small. Much higher accelerations, such as when a pair of heavy ions suffer an ultra peripheral collision, cause substantial emission of various excited vector mesons. Predictions are made for the spectrum of this radiation. A comparison is made against existing photon-pomeron fusion calculations for the transverse momentum spectra of rho mesons. These have the same overall shape as the recently measured transverse momentum distributions at RHIC.

hep-ph↗
arXiv2006

Two-Photon Effects in Lepton-AntiLepton Pair Photoproduction from a Nucleon Target using Real Photons

We consider the production of a lepton-antilepton pair by real photons off a hadronic target. The interference of one and two photon exchange amplitudes leads to a charge asymmetry term that may be calculated explicitly in the large-t limit in terms of hadronic distribution amplitudes. A rather compact expression emerges for the leading order asymmetry at fixed angle in the centre-of-mass of the lepton pair. The magnitude appears sizeable and is approximately independent of the pair mass in the asymptotic limit.

hep-ph↗
arXiv2005

The Casimir Effect Upon A Single Plate

In the presence of an external field, the imposition of specific boundary conditions can lead to interesting new manifestations of the Casimir effect. In particular, it is shown here that even a single conducting plate may experience a non-zero force due to vacuum fluctuations. The origins of this force lie in the change induced by the external potential in the density of available quantum states.

quant-ph↗
arXiv2003

Probing Quark Distribution Amplitudes Through Generalized Parton Distributions at Large Momentum Transfer

In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively-calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the $H_q(x,ξ,t)$ distribution for the pion and proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result can also be used as a constraint in phenomenological GPD parametrizations.

hep-ph↗
arXiv1999

Does the Gluon Spin Contribute in A Gauge Invariant Way to Nucleon Spin?

Although the matrix element of the gluon spin operator in nucleon helicity states is known to be independent of some special choices of gauge, we show that it is not invariant under a general gauge transformation. We find that there exists a simple means of obtaining the matrix element in a different choice of gauge from a calculation made in one specific gauge. Similar conclusions hold for other manifestly gauge-dependent operators present in the QCD angular momentum operator.

hep-ph↗
arXiv1999

Electroproduction of Transversely Polarized Vector Mesons Via A Quantum Mechanical Anomaly

By explicit calculation we demonstrate that, in variance with the classical prediction, the leading twist contribution to the exclusive electroproduction of transversely polarized vector mesons from the nucleon does not vanish beyond the leading order in perturbation theory. This appears to be due to a quantum-mechanical anomaly, in the sense that a classical symmetry of the field theory is broken by quantum corrections.

hep-ph↗
arXiv1998

Implications of Color Gauge Symmetry For Nucleon Spin Structure

We study the chromodynamical gauge symmetry in relation to the internal spin structure of the nucleon. We show that 1) even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element; 2) the evolution equations for the gluon spin take very different forms in the Feynman and axial gauges, but yield the same leading behavior in the asymptotic limit; 3) the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the light-cone gauge. We define a new gluon orbital angular momentum distribution $L_g(x)$ which {\it is} an experimental observable and has a simple scale evolution. However, its physical interpretation makes sense only in the light-cone gauge just like the gluon helicity distribution $Δg(x)$y.

hep-ph↗
arXiv1998

Quark Orbital-Angular-Momentum Distribution in the Nucleon

We introduce gauge-invariant quark and gluon angular momentum distributions after making a generalization of the angular momentum density operators. From the quark angular momentum distribution, we define the gauge-invariant and leading-twist quark {\it orbital} angular momentum distribution $L_q(x)$. The latter can be extracted from data on the polarized and unpolarized quark distributions and the off-forward distribution $E(x)$ in the forward limit. We comment upon the evolution equations obeyed by this as well as other orbital distributions considered in the literature.

hep-ph↗
arXiv1998

Helicity-Flip Off-Foward Parton Distributions of the Nucleon

We identify quark and gluon helicity-flip distributions defined between nucleon states of unequal momenta. The evolution of these distributions with change of renormalization scale is calculated in the leading-logarithmic approximation. The helicity-flip gluon distributions do not mix with any quark distribution and are thus a unique signature of gluons in the nucleon. Their contribution to the generalized virtual Compton process is obtained both in the form of a factorization theorem and an operator product expansion. In deeply virtual Compton scattering, they can be probed through distinct angular dependence of the cross section.

hep-ph↗
arXiv1997

Wavefunction corrections and off-forward gluon distributions in diffractive $J/ψ$ electroproduction

Diffractive production of $J/Ψ$ particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importance of the off-forwardness, we compute, in leading order perturbation theory, the extent of deviation from the usual forward gluon distribution in a quark.

hep-ph↗
arXiv1996

Wavefunction corrections and off-forward gluon distributions in diffractive J/psi electroproduction

Diffractive production of J/Psi particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importance of the off-forwardness, we compute, in leading order perturbation theory, the extent of deviation from the usual forward gluon distribution in a quark.

hep-ph↗