Quantum Effective Potential Research Articles

Effective potential in finite formulation of QFT

In recent works [1,2], we have shown how n-point correlation functions in perturbative QFT can be computed without running into intermediate divergences. Here we want to illustrate explicitly that one can calculate the quantum effective potential by the same method. As a main example, we consider a theory with two fields having large and small vacuum expectation values (vev). We show that no fine-tuning between the physical quantities is needed to keep the hierarchy between the vevs of different fields.

Effective potential and vacuum stability in the Litim-Sannino model

We revisit the scalar potential in the Litim-Sannino model. We compute for the first time the full quantum corrections to the classical potential and show that they significantly ameliorate the stability analysis at the UV fixed point. The quantum effective potential is computed at two-loop order and the numerical precision is further improved using resummations and parameter optimisations. As a result, we find a consistent widening of the UV conformal window across various approximations.

Quantum heat machines enabled by twisted geometry

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines, with an incompressible sample, can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.

Goldstino condensation at large N

We analyze the standard fermionic 4D Volkov–Akulov action with N global non-linear supersymmetries. We find that the stationary points of the system are described by an effective potential, written in terms of two composite real scalar fields, which approaches the exact quantum effective potential in the large N limit. We identify the existence of at least two stationary points, one representing the original supersymmetry breaking configuration and the other one corresponding to goldstino condensation, where supersymmetry is restored in the deep IR.

Semiclassical trajectories in the double-slit experiment

We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.

Photofragmentation of I2 molecules inside helium clusters: model calculations using a quantum effective potential

We report the results of model calculations for the photodissociation of iodine molecules inside liquid helium clusters composed of several thousand atoms. The helium clusters are described by a quantum effective potential between helium atoms. Classical trajectories are run with this potential model in order to determine excitation energy thresholds for caging of atomic iodine fragments followed by recombination or, alternatively, production of photofragments which leave the helium cluster. Typical photofragments are iodine atoms carrying along a certain number of helium atoms. The computed photofragment velocity and size distributions for several cluster sizes compare favourably with experimental observations for related molecular systems.

Quantum corrections to slow-roll inflation: scalar and tensor modes

Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified with the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.

Application of localization landscape theory and the k · p model for direct modeling of carrier transport in a type II superlattice InAs/InAsSb photoconductor system

Localization landscape (LL) theory is applied to directly model carrier transport in a type II superlattice (T2SL) InAs/InAsSb photoconductor system. It is difficult to apply the classical Poisson and drift–diffusion (DD) model to direct modeling of carrier transport in superlattice systems because quantum effects need to be considered. With the LL theory, it is possible to obtain the effective quantum potential seen by carriers. By coupling the LL theory with the Poisson–DD model and replacing the traditional conduction and valence potentials with effective quantum potentials, it is possible to directly model carrier transport in a T2SL system. We compare the results of this approach with experimental results and find very good agreement, which indicates that this method will provide an efficient tool for the T2SL design.

The large N phase diagram of mathcal{N} = 2 SU(N) Chern-Simons theory with one fundamental chiral multiplet

We study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large N limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the ’t Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large N mathcal{N} = 2 supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general mathcal{N} = 1 supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an SU(N ) Chern-Simons gauge field, at arbitrary values of the ’t Hooft coupling.

Tricritical behavior in a Chern-Simons gauge field theory

I describe a condensed matter system in terms of interacting quantum fields. In this electronic system, gauge interactions of non electromagnetic origin are generated effectively with a topological term in the effective action and play a leading role in describing the physics. Using the renormalization group and large-N expansion technique, I analyze the low energy sector of a U(1) × U(1) model in three dimensional space-time with a potential of sixth order in the scalar fields coupled to mixed Chern-Simons gauge fields. From the quantum effective potential, I derive various renormalization group functions and the fixed points associated with a quantum phase transition.

Holographic RG flows on curved manifolds and the F-theorem

We study F-functions in the context of field theories on S3 using gauge-gravity duality, with the radius of S3 playing the role of RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good F-functions, which decrease monotonically along the RG flow from the UV to the IR for a wide range of examples. If the operator perturbing the UV CFT has dimension Δ > 3/2 these F -functions correspond to an appropriately renormalized free energy. If instead the perturbing operator has dimension Δ < 3/2 it is the quantum effective potential, i.e. the Legendre transform of the free energy, which gives rise to good F-functions. We check that these observations hold beyond holography for the case of a free fermion on S3 (Δ = 2) and the free boson on S3 (Δ = 1), resolving a long-standing problem regarding the non-monotonicity of the free energy for the free massive scalar. We also show that for a particular choice of entangling surface, we can define good F-functions from an entanglement entropy, which coincide with certain F-functions obtained from the on-shell action.

Topologically Stable States of the Anti-Centrifugal Potential

We present a study of the anti-centrifugal potential based on the incorporation of the quantum geometric potential of a surface [1] into the generalised anti-centrifugal potential [2]. As a basic variable we will use the unit normal to the surface. Then the total quantum effective potential appears to be the nonlinear sigma model plus positive terms. A 2d bilayer geometry smoothly connected by a neck is used to show that the anti-centrifugal potential creates topologically stable states.

Quantum No-Scale Regimes and String Moduli

We review that in no-scale models in perturbative string theory, flat, homogeneous and isotropic cosmological evolutions found at the quantum level can enter into “quantum no-scale regimes” (QNSRs). When this is the case, the quantum effective potential is dominated by the classical kinetic energies of the no-scale modulus, dilaton and moduli not involved in the supersymmetry breaking. As a result, the evolutions approach the classical ones, where the no-scale structure is exact. When the one-loop potential is positive, a global attractor mechanism forces the initially expanding solutions to enter the QNSR describing a flat, ever-expanding universe. On the contrary, when the potential can reach negative values, the internal moduli induce in most cases some kind of instability of the growing universe. The latter stops expanding and eventually collapses, unless the initial conditions are tuned in a tiny region of the phase space. Finally, in QNSR, no gauge instability takes place, regardless of the details of the potential.

Three dimensional simulation on the transport and quantum efficiency of UVC-LEDs with random alloy fluctuations

The active regions of ultraviolet light emitting diodes (UVLEDs) for UVB and ultra-violet band C wavelengths are composed of AlGaN alloy quantum barriers (QBs) and quantum wells (QWs). The use of alloy QBs and QWs facilitates the formation of percolative paths for carrier injection but also decreases carrier confinement within the QWs. We applied the recently developed Localization Landscape (LL) theory for a full 3D simulation of the LEDs. LL theory describes the effective quantum potential of the quantum states for electrons and holes in a random disordered system with a high computational speed. The results show that the potential fluctuations in the n-AlGaN buffer layer, QWs, and QBs provide percolative paths for carrier injection into the top (p-side) QW. Several properties due to compositional disorder are observed: (1) The peak internal quantum efficiency is larger when disorder is present, due to carrier localization, than for a simulation without fluctuations. (2) The droop is larger mainly due to poor hole injection and weaker blocking ability of the electron blocking layer caused by the fluctuating potentials. (3) Carriers are less confined in the QW and extend into the QBs due to the alloy potential fluctuations. The wave function extension into the QBs enhances TM emission as shown from a k·p simulation of wave-functions admixture, which should then lead to poor light extraction.

Quantum effective potential from discarded degrees of freedom

I obtain the quantum correction ΔVeff=(ħ2/8m)[(1−4ξd+1d)(S′)2+2(1−4ξ)S″] that appears in the effective potential whenever a compact d-dimensional subspace (of volume ∝exp⁡[S(x)]) is discarded from the configuration space of a nonrelativistic particle of mass m and curvature coupling parameter ξ. This correction gives rise to a force −〈ΔVeff′〉 that pushes the expectation value 〈x〉 off its classical trajectory. Because ΔVeff does not depend on the details of the discarded subspace, these results constitute a generic model of the quantum effect of discarded variables with maximum entropy/information capacity S(x).

Quantum no-scale regimes in string theory

We show that in generic no-scale models in string theory, the flat, expanding cosmological evolutions found at the quantum level can be attracted to a “quantum no-scale regime”, where the no-scale structure is restored asymptotically. In this regime, the quantum effective potential is dominated by the classical kinetic energies of the no-scale modulus and dilaton. We find that this natural preservation of the classical no-scale structure at the quantum level occurs when the initial conditions of the evolutions sit in a subcritical region of their space. On the contrary, supercritical initial conditions yield solutions that have no analogue at the classical level. The associated intrinsically quantum universes are sentenced to collapse and their histories last finite cosmic times. Our analysis is done at 1-loop, in perturbative heterotic string compactified on tori, with spontaneous supersymmetry breaking implemented by a stringy version of the Scherk–Schwarz mechanism.

Sticking to (first) principles: quantum molecular dynamics and Bayesian probabilistic methods to simulate aquatic pollutant absorption spectra.

This work explores the relationship between theoretically predicted excitation energies and experimental molar absorption spectra as they pertain to environmental aquatic photochemistry. An overview of pertinent Quantum Chemical descriptions of sunlight-driven electronic transitions in organic pollutants is presented. Second, a combined molecular dynamics (MD), time-dependent density functional theory (TD-DFT) analysis of the ultraviolet to visible (UV-Vis) absorption spectra of six model organic compounds is presented alongside accurate experimental data. The functional relationship between the experimentally observed molar absorption spectrum and the discrete quantum transitions is examined. A rigorous comparison of the accuracy of the theoretical transition energies (ΔES0→Sn) and oscillator strength (fS0→Sn) is afforded by the probabilistic convolution and deconvolution procedure described. This method of deconvolution of experimental spectra using a Gaussian Mixture Model combined with Bayesian Information Criteria (BIC) to determine the mean (μ) and standard deviation (σ) as well as the number of observed singlet to singlet transition energy state distributions. This procedure allows a direct comparison of the one-electron (quantum) transitions that are the result of quantum chemical calculations and the ensemble of non-adiabatic quantum states that produce the macroscopic effect of a molar absorption spectrum. Poor agreement between the vertical excitation energies produced from TD-DFT calculations with five different functionals (CAM-B3LYP, PBE0, M06-2X, BP86, and LC-BLYP) suggest a failure of the theory to capture the low energy, environmentally important, electronic transitions in our model organic pollutants. However, the method of explicit-solvation of the organic solute using the quantum Effective Fragment Potential (EFP) in a density functional molecular dynamics trajectory simulation shows promise as a robust model of the hydrated organic pollutant. Furthermore, the described protocol can be extended using higher-level equilibration and vertical excitation methods to increase the numerical accuracy and describe multi-reference electronic transitions. Finally, a measure of the accuracy of theoretically derived absorption spectra is discussed as a tool to further develop our capacity to produce accurate a priori simulations of sunlight-driven photochemistry in natural waters.

Helicoidal graphene nanoribbons: Chiraltronics

We present a calculation of the effective geometry-induced quantum potential for the carriers in graphene shaped as a helicoidal nanoribbon. In this geometry the twist of the nanoribbon plays the role of an effective transverse electric field in graphene and this is reminiscent of the Hall effect. However, this effective electric field has a different sign for the two iso-spin states and translates into a mechanism to separate the two chiral species on the opposing rims of the nanoribbon. Iso-spin transitions are expected with the emission or absorption of microwave radiation which could be adjusted to be in the THz region.

The holographic quantum effective potential at finite temperature and density

Abstract We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for studying the ground state of the theory, symmetry breaking patterns and phase transitions. We derive general formulae for the effective potential and apply them to determine the phase transition temperature and density in the scaling region.

Heterochiral Domain Formation in Homochiral α-Dipalmitoylphosphatidylcholine (DPPC) Langmuir Monolayers at the Air/Water Interface

α-Dipalmitoylphosphatidylcholine (DPPC) Langmuir monolayers at the air/water interface are an important biomimetic system. Previous studies using optical imaging have shown that enantiomerically pure DPPC molecules form periodical homochiral domains with close packing. However, it is unclear whether the chirality of these domains is stable or dynamic. Recently, we investigated the chirality of l-DPPC Langmuir monolayers using second-harmonic-generation linear dichroism (SHG-LD). The change in the degree of chiral excess (DCE) and its sign with time indicated that the chirality transformed from homochiral to heterochiral domains, with an associated change in handedness. Here we propose that hydrolysis of l-DPPC is responsible for the formation of the opposite chiral state. On the basis of quantum chemistry calculations and effective pair potential (EPP) theory, we give a molecular explanation for this transformation. These results provide an insight into the lipid monolayers that the chiral state of domains composed of chiral lipids is dynamic.