Non-vanishing Expectation Value Research Articles

Observing Majorana Fermion dynamic properties on a NISQ computer

Majorana particles are of particular interest due to their profound property of being their own anti-particles and potential applications for quantum computers. However, studying the dynamics of Majorana particles experimentally has proven to be challenging, with many unanswered questions about their behaviors. In this paper, we demonstrate that an improved discrete-time quantum walks (DTQW) on a Noisy Intermediate-Scale Quantum (NISQ) computer can be used to construct a well-defined Majorana fermion. Through this approach, we can observe the behaviors of Majorana particle propagation both in (1+1)- and (3+1)-dimensions. A counter-intuitive dynamic behavior of the non-vanishing expectation value of velocity and position with zero expectation value of momentum from the superposition of positive and negative energy solution is observed for the first time in NISQ. Our findings provide a promising avenue for experimentally studying the dynamical properties of Majorana particles.

Cellular automaton for spinor gravity in four dimensions

Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive continuum limit. Our setting could serve as a model for quantum gravity if diffeomorphism symmetry is realized in the true continuum limit and suitable collective fields for vierbein and metric acquire non-vanishing expectation values. The discussion of this interesting specific model reveals may key qualitative features of the continuum limit for probabilistic cellular automata. This limit obtains for a very large number of cells if the probabilistic information is sufficiently smooth. It is associated to coarse graining. The automaton property that every bit configuration is updated at every discrete time step to precisely one new bit configuration does no longer hold on the coarse grained level. A coarse grained configuration of occupation numbers can evolve into many different configurations with certain probabilities. This characteristic feature of quantum field theories can come along with the emergence of continuous space-time symmetries.

The generalized first law for more general matter

In previous work, a first law of generalized entropy was derived from semiclassical gravitational dynamics around thermal setups using an assumed relation between the matter modular Hamiltonian and the gravitational stress tensor. Allowing for non-minimal coupling between curvature and any tensor matter fields, we show however, that the modular Hamiltonian of thermal states is given by the integrated bulk Noether current associated to time translation plus a spacetime boundary term. One generally cannot express this in terms of gravitational stress tensor components. Still, working with the correct expression for the modular Hamiltonian, we are able to recover a first law of generalized entropy, with added benefits over the previous result. Firstly, any Wald-Dong contributions to generalized entropy resulting from non-minimal coupling between matter and curvature are included. Secondly, in gravitational equations of motion, we allow for a non-vanishing stress tensor expectation value in the unperturbed background and state, and account for background field perturbations as part of its variation. Finally, the quantum matter is allowed to contribute nontrivially to asymptotic energy, e.g. as is necessary, even for a minimally coupled Maxwell field, to recover the expected thermodynamic first law of charged black holes.

Unitary Kinematic Mixing of Electro-Weak Bosons

In the standard model, electro-weak bosons are developed as gauge-fields initially satisfying an SU(2) $\times$ U(1) local symmetry mediating interactions with a multi-component field. This symmetry gets broken when the component of the field associated with the (scalar) Higgs boson acquires a non-vanishing expectation value, generating masses for weak vector bosons (W$^+$,W$^-$,Z) as well as a massless photon (A) which couples to electric charge. Beyond an expression relating the masses of the W and Z bosons, there are few predictions concerning further relationships involving the Higgs mass or mixing angle. In this paper, kinematic relationships between unitarily mixed momentum-space spinors (supplemental to standard electro-weak modeling) will be developed. These relationships expressed in terms of kinematic invariants are shown to be consistent with current measured results.

Unified Dark Matter, Dark Energy and baryogenesis via a “cosmological wetting transition”

In a recent publication [1], a cosmological scenario featuring a scalar field, φ, that is a source for Dark Matter and Dark Energy has been proposed. In this paper, a concrete realization of that scenario is presented. As in many models of scalar-field driven Dark Energy, the effective Lagrangian of the field φ contains a potential proportional to e−φ/f. This potential is modulated in such a way that, in the absence of other matter fields, it has a local minimum at a small value of φ. Fluctuations of φ around this minimum give rise to a gas of dark-matter particles. The field φ is coupled to another scalar field χ in such a way that the minimum in the effective potential of φ disappears when, after a continuous phase transition accompanied by spontaneous symmetry breaking, χ develops a non-vanishing expectation value. This triggers slow growth of a homogeneous component of φ accompanied by the emergence of Dark Energy, a phenomenon analogous to the “wetting transition” in statistical mechanics. Inside regions of the Universe where the pressure is small and the energy density is large enough to stall expansion, in particular around galaxies and galaxy clusters, the phase transition in the state of χ does not take place, and a gas of cold dark-matter particles persists. The evolution of φ at very early times may tune the rate of baryogenesis.

Constraining quantum collapse inflationary models with current data: The semiclassical approach

The hypothesis of the self-induced collapse of the inflaton wave function was introduced as a candidate for the physical process responsible for the emergence of inhomogeneity and anisotropy at all scales. In particular, we consider different proposal for the precise form of the dynamics of the inflaton wave function: (i) the GRW-type collapse schemes proposals based on spontaneous individual collapses which generate nonvanishing expectation values of various physical quantities taken as ansatz modifications of the standard inflationary scenario; (ii) the proposal based on a Continuous Spontaneous Localization (CSL) type modification of the Schrödinger evolution of the inflaton wave function, based on a natural choice of collapse operator. We perform a systematic analysis within the semi-classical gravity approximation, of the standing of those models considering a full quasi-de Sitter expansion scenario. We note that the predictions for the Cosmic Microwave Background (CMB) temperature and polarization spectrum differ slightly from those of the standard cosmological model. We also analyze these proposals with a Bayesian model comparison using recent CMB and Baryonic Acoustic Oscillations (BAO) data. Our results show a moderate preference of the joint CMB and BAO data for one of the studied collapse schemes model over the [Formula: see text]CDM one, while there is no preference when only CMB data are considered. Additionally, analysis using CMB data provide the same Bayesian evidence for both the CSL and Standard Models, i.e. the data have no preference between the simplicity of the LCDM model and the complexity of the collapse scenario.

Leptogenesis in inflationary models with non-Abelian gauge fields

A scenario of leptogenesis was introduced in [1] which works during inflationary period within standard model of particle physics setup. In this scenario lepton number is created by the gravitational chiral anomaly which has a non-zero expectation value for models of inflation driven by pseudoscalar field(s). Here, we observe that models of inflation involving non-Abelian gauge fields, e.g. the chromo-natural inflation [2] or the gauge-flation [3], have a parity-violating tensor mode (graviton) spectrum and naturally lead to a non-vanishing expectation value for the gravitational chiral anomaly. Therefore, one has a natural leptogenesis scenario associated with these inflationary setups, \emph{inflato-natural leptogenesis}. We argue that the observed value of baryon-to-photon number density can be explained in a natural range of parameters in these models.

Symmetry breaking, and the effect of matter density on neutrino oscillation

A proposal for the neutrino mass, based on neutrino-scalar field interaction, is introduced. The scalar field is also non-minimally coupled to the Ricci scalar, and hence relates the neutrino mass to the matter density. In a dense region, the scalar field obeys the Z2 symmetry, and the neutrino is massless. In a dilute region, the Z2 symmetry breaks and neutrino acquires mass from the non-vanishing expectation value of the scalar field. We consider this scenario in the framework of a spherical dense object whose outside is a dilute region. In this background, we study the neutrino flavors oscillation, along with the consequences of the theory on oscillation length and MSW effect. This preliminary model may shed some lights on the existing anomalies within the neutrino data, concerning the different oscillating behavior of the neutrinos in regions with different densities.

Nonperturbative mechanism for elementary particle mass generation

Taking inspiration from lattice QCD data, we argue that a finite non-perturbative contribution to the quark mass is generated as a consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn triggered by the explicitly breaking of chiral symmetry induced by the critical Wilson term in the action. In pure lattice QCD this mass term cannot be separated from the unavoidably associated linearly divergent contribution. However, if QCD is enlarged to a theory where also a scalar field is present, coupled to an SU(2) doublet of fermions via a Yukawa and a Wilson-like term, then in the phase where the scalar field takes a non-vanishing expectation value, a dynamically generated and "naturally" light fermion mass (numerically unrelated to the expectation value of the scalar field) is conjectured to emerge at a critical value of the Yukawa coupling where the symmetry of the model is maximally enhanced. Masses dynamically generated in this way display a natural hierarchy according to which the stronger is the strongest of the interactions the fermion is subjected to the larger is its mass.

Parity-violating effects in an exotic perturbation of the rigid rotator

The perturbation of the free rigid rotator by the trigonometric Scarf potential is shown to conserve its energy excitation patterns and change only the wave functions towards spherical harmonics rescaled by a function of an unspecified parity, or mixtures of such rescaled harmonics of equal magnetic quantum numbers and different angular momenta. In effect, no parity can be assigned to the states of the rotational bands emerging in this exotic way, and the electric dipole operator is allowed to acquire non-vanishing expectation values.

Loop quantization of a model for D = 1 + 2 (anti)de Sitter gravity coupled to topological matter

We present a complete quantization of Lorentzian gravity with cosmological constant, coupled to a set of topological matter fields. The approach of loop quantum gravity is used thanks to a partial gauge fixing leaving a residual gauge invariance under a compact semi-simple gauge group, namely Spin(4) = SU(2) × SU(2). A pair of quantum observables is constructed, which are non-trivial despite being gauge-equivalent to zero at the classical level. A semi-classical approximation based on appropriately defined coherent states shows non-vanishing expectation values for them, thus not reproducing their classical behaviour.

Spontaneous R-parity breaking, stop LSP decays and the neutrino mass hierarchy

The MSSM with right-handed neutrino supermultiplets, gauged B−L symmetry and a non-vanishing sneutrino expectation value is the minimal theory that spontaneously breaks R-parity and is consistent with the bounds on proton stability and lepton number violation. This minimal B−L MSSM can have a colored/charged LSP, of which a stop LSP is the most amenable to observation at the LHC. We study the R-parity violating decays of a stop LSP into a bottom quark and charged leptons – the dominant modes for a generic “admixture” stop. A numerical analysis of the relative branching ratios of these decay channels is given using a wide scan over the parameter space. The fact that R-parity is violated in this theory by a vacuum expectation value of a sneutrino links these branching ratios directly to the neutrino mass hierarchy. It is shown how a discovery of bottom-charged lepton events at the LHC can potentially determine whether the neutrino masses are in a normal or inverted hierarchy, as well as determining the θ23 neutrino mixing angle. Finally, present LHC bounds on these leptoquark signatures are used to put lower bounds on the stop mass.

Chiral Condensate and the Structure of Hadrons

Spontaneous chiral symmetry breaking is, apart from colour confinement, the most important physical aspect of strong interactions. Virtual quarks and antiquarks of opposite chirality are attracted to each other due to the strong interactions and destabilize the trivial vacuum state. A condensate is formed which gives rise to a nonvanishing expectation value of the bilinear fermionic operator ψψ. Once the temperature is raised, chiral symmetry will be affected and eventually restored in the deconfined phase of QCD. In order to find the temperature dependence of the chiral condensate in the hadronic medium, we use the framework of the hadron resonance gas (HRG) with the partition function ZHRG. From the generic definition follows in this case 〈qq〉 = − ∂ ∂m0 T lnZHRG = 〈qq〉0 + ∑

Gravitational modulated reheating and non-Gaussianity in supergravityR2inflation

Reheating after ${R}^{2}$ inflation proceeds through gravitational particle production of conformally noninvariant fields. We argue that the nonvanishing expectation value of flat directions generic in supersymmetric theories break conformal invariance of the fields coupled to them in a position-dependent manner due to quantum fluctuations. As a result modulated reheating can occur after the supergravity ${R}^{2}$-inflation. The resultant curvature fluctuation is a mixture of the one produced during inflation and that produced by modulated reheating. The spectral index takes a value between ${n}_{s}=0.960$ and 0.983, the nonlinearity parameter of the local-type non-Gaussianity can be ${f}_{\mathrm{NL}}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}10$, and the tensor-to-scalar ratio is $r\ensuremath{\le}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

On the fate of coupled flat directions during inflation

We investigate the stochastic dynamics of the long wavelength modes of a generic light scalar field that during inflation is coupled to another scalar field. The coupling plays an important role for the fluctuation of the field amplitude and may block its initial growth. We find that such a blocking is avoided, albeit only temporarily, if the light scalar has an initial non-vanishing expectation value ⟨ϕ⟩ larger than a certain critical value, for which we provide an estimate. We also show that the field fluctuations will eventually reach an equilibrium amplitude provided inflation is sufficiently long-lasting. We present a novel, general expression for the variance ⟨ϕ2⟩ that takes into account the coupling of the massless field and describes the growth during the epoch of quasi-free fluctuations as well as the late-time approach to the equilibrium.

An all-order proof of the equivalence between Gribovʼs no-pole and Zwanzigerʼs horizon conditions

The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev–Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang–Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribovʼs no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanzigerʼs horizon function. The action allowing to implement this condition is the Gribov–Zwanziger action. This establishes in a precise way the equivalence between Gribovʼs no-pole condition and Zwanzigerʼs horizon condition.

Emergent gravity in two dimensions

We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice diffeomorphism invariance which ensures in the continuum limit the symmetry of general coordinate transformations. We observe a collective order parameter with properties of a metric, showing Minkowski or Euclidean signature. The correlation functions of the metric reveal an interesting long-distance behavior with power-like decay. This universal critical behavior occurs without tuning of parameters and thus constitutes an example of “self-tuned criticality” for this type of sigma-models. We also find a non-vanishing expectation value of a “zweibein” related to the “internal” degrees of freedom of the scalar field, again with long-range correlations. The metric is well described as a composite of the zweibein. A scalar condensate breaks Euclidean rotation symmetry.

Spontaneous breakdown of Lorentz symmetry in scalar QED with higher order derivatives

Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar field and the vector potential is constructed in the leading order saddle point expansion. This vacuum breaks the global gauge and Lorentz symmetry spontaneously. The unitarity of time evolution is assured in the physical, positive norm subspace and the linearized equations of motion are calculated. Goldstone theorem always keeps the radiation field massless. A particular model is constructed where the the full set of standard Maxwell equations is recovered on the tree level thereby relegating the effects of broken Lorentz symmetry to the level of radiative corrections.

Broken symmetry phase solution of theϕ4model at two-loop level of theΦ-derivable approximation

The set of coupled equations for the self-consistent propagator and the field expectation value is solved numerically with high accuracy in Euclidean space at zero temperature and in the broken symmetry phase of the phi^4 model. Explicitly finite equations are derived with the adaptation of the renormalization method of van Hees and Knoll [H. van Hees, J. Knoll, Phys. Rev. D65, 025010 (2001)] to the case of non-vanishing field expectation value. The set of renormalization conditions used in this method leads to the same set of counterterms obtained recently in A. Patkos, Zs. Szep, Nucl. Phys. A811, 329-352 (2008). This makes possible the direct comparison of the accurate solution of explicitly finite equations with the solution of renormalized equations containing counterterms. The numerically efficient way of solving iteratively these latter equations is obtained by deriving at each order of the iteration new counterterms which evolve during the iteration process towards the counterterms determined based on the asymptotic behavior of the converged propagator. As shown at different values of the coupling, the use of these evolving counterterms accelerates the convergence of the solution of the equations.

Broken phase scalar effective potential andΦ-derivable approximations

We study the effective potential of a real scalar phi^4 theory as a function of the temperature T within the simplest Phi-derivable approximation, namely the Hartree approximation. We apply renormalization at a "high" temperature T* where the theory is required to be in its symmetric phase and study how the effective potential evolves as the temperature is lowered down to T=0. In particular, we prove analytically that no second order phase transition can occur in this particular approximation of the theory, in agreement with earlier studies based on the numerical evaluation or the high temperature expansion of the effective potential. This work is also an opportunity to illustrate certain issues on the renormalization of Phi-derivable approximations at finite temperature and non-vanishing field expectation value, and to introduce new computational techniques which might also prove useful when dealing with higher order approximations.