Large Parameter Region Research Articles

Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes

We propose families of protocols for magic state distillation -- important components of fault tolerance schemes --- for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that, in higher dimensions, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. The five-dimensional protocol is, by many measures, the best magic state distillation scheme yet discovered. It excels both in terms of error threshold with respect to depolarising noise (36.3%) and the efficiency measure know as "yield", where, for a large region of parameters, it outperforms its qubit counterpart by many orders of magnitude.

The epidemiological consequences of leprosy-tuberculosis co-infection

While in antiquity both leprosy and tuberculosis were prevalent in Europe, leprosy declined thereafter and, simultaneously, tuberculosis prevalence increased. Since both diseases are caused by mycobacterial infections, it has been suggested that there might be a causal relationship between both epidemics.Chaussinand observed the inverse prevalence of leprosy and tuberculosis and suggested that individuals with a latent tuberculosis infection are protected from acquiring leprosy. His cross-immunity hypothesis has been countered more recently by a co-infection hypothesis. The latter suggestion, proposed by Donoghue, states that people being infected with multi-bacillary leprosy are more susceptible to tuberculosis, which leads to increased mortality from the disease.This study utilizes mathematical modeling to explore the epidemiological consequences of the co-infection hypothesis for realistically confined parameter values. While the co-infection hypothesis appears plausible at first glance, a second thought reveals that it comprises also substantial consequences for tuberculosis epidemics: if co-infection raises the mortality rate above that of purely tuberculosis infected persons, then tuberculosis might as well be eradicated by leprosy. It is the specific interplay of both increased susceptibility towards tuberculosis and increased death rate when co-infected that determines the epidemiological fate.As a result of this analysis, it is shown that there is a large parameter region where the eventual disappearance of leprosy could indeed be explained by co-infection. This parameter region is considerably larger than that predicted by the cross-immunity hypothesis. This shows that the co-infection hypothesis should be considered a significant alternative to the cross-immunity hypothesis. The time scales at which the effects of co-infection are observed depend critically on the spatial distribution of the individuals but reach epidemiologically realistic values for rather immobile individuals with local interaction.

Discrete solitons in -symmetric lattices

We prove the existence of discrete solitons in infinite parity-time () symmetric lattices by means of analytical continuation from the anticontinuum limit. The energy balance between dissipation and gain implies that in the anticontinuum limit the solitons are constructed from elementary -symmetric blocks such as dimers, quadrimers, or more general oligomers. We consider in detail a chain of coupled dimers, analyze bifurcations of discrete solitons from the anticontinuum limit and show that the solitons are stable in a sufficiently large region of the lattice parameters. The generalization of the approach is illustrated on two examples of networks of quadrimers, for which stable discrete solitons are also found.

Loss of Time Delay Signature in Broadband Cascade-Coupled Semiconductor Lasers

Numerical and experimental investigations of time delay concealment and chaos bandwidth enhancement in three semiconductor lasers with a cascade scheme are presented. The cascade system is composed of an external-cavity master laser, a solitary intermediate laser, and a solitary slave laser. The results show that the first two lasers are used for concealing time delay signature, and the last two lasers are used for bandwidth enhancement. For large parameter regions of injection strength and frequency detuning, time delay concealment and bandwidth enhancement of chaotic signals are simultaneously achieved by adopting the simple cascade configuration.

Probing new physics viapp→W+W−→lνjjat the CERN LHC

TeV scale new physics, e.g., large extra dimensions or models with anomalous triple vector boson couplings, can lead to excesses in various kinematic regions on the semileptonic productions of $pp\ensuremath{\rightarrow}WW\ensuremath{\rightarrow}l\ensuremath{\nu}jj$ at the CERN LHC, which, although suffer from large QCD background compared with the pure leptonic channel $pp\ensuremath{\rightarrow}WW\ensuremath{\rightarrow}l\ensuremath{\nu}l\ensuremath{\nu}$, can benefit from larger production rates and the reconstructable four-body mass ${M}_{l\ensuremath{\nu}jj}$. We study the search sensitivity through the $l\ensuremath{\nu}jj$ channel at the 7 TeV LHC on relevant new physics via probing the hard tails on the reconstructed ${M}_{l\ensuremath{\nu}jj}$ and the transverse momentum of leptonically decayed $W$ boson (${P}_{TW}$), taking into account main backgrounds and including the parton shower and detector simulation effects. Our results show that with integrated luminosity of $5\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, the LHC can already discover or exclude a large parameter region of the new physics, e.g., a 95% C.L. can be set on the large extra dimensions with a cutoff scale up to 1.5 TeV, and the $WWZ$ anomalous coupling down to, e.g., $|{\ensuremath{\lambda}}_{Z}|\ensuremath{\sim}0.1$. Results are also given for the 8 TeV LHC.

Cosmology of a scalar field coupled to matter and an isotropy-violating Maxwell field

Motivated by the couplings of the dilaton in four-dimensional effective actions, we investigate the cosmological consequences of a scalar field coupled both to matter and a Maxwell-type vector field. The vector field has a background isotropy-violating component. New anisotropic scaling solutions which can be responsible for the matter and dark energy dominated epochs are identified and explored. For a large parameter region the universe expands almost isotropically. Using that the CMB quadrupole is extremely sensitive to shear, we constrain the ratio of the matter coupling to the vector coupling to be less than 10^(-5). Moreover, we identify a large parameter region, corresponding to a strong vector coupling regime, yielding exciting and viable cosmologies close to the LCDM limit.

Nonperturbative dynamical decoupling control: A spin-chain model

This paper considers a spin-chain model by numerically solving the exact model to explore the nonperturbative dynamical decoupling regime, where an important issue recently arose. Our study has revealed a few universal features of nonperturbative dynamical control irrespective of the types of environments and system-environment couplings. We have shown that, for the spin-chain model, there is a threshold and a large pulse parameter region where the effective dynamical control can be implemented, in contrast to the perturbative decoupling schemes where the permissible parameters are represented by a point or converge to a very small subset in the large parameter region admitted by our nonperturbative approach. An important implication of the nonperturbative approach is its flexibility in implementing the dynamical control scheme in an experimental setup. Our findings have exhibited several interesting features of the nonperturbative regimes such as the chain-size independence, pulse strength upper bound, noncontinuous valid parameter regions, etc. Furthermore, we find that our nonperturbative scheme is robust against randomness in model fabrication and time-dependent random noise.

Quantification of memory effects in the spin-boson model

Employing a recently proposed measure for quantum non-Markovianity, we carry out a systematic study of the size of memory effects in the spin-boson model for a large region of temperature and frequency cutoff parameters. The dynamics of the open system is described utilizing a second-order time-convolutionless master equation without the Markov or rotating wave approximations. While the dynamics is found to be strongly non-Markovian for low temperatures and cutoffs, in general, we observe a special regime favoring Markovian behavior. This effect is explained as resulting from a resonance between the system's transition frequency and the frequencies of the dominant environmental modes. We further demonstrate that the corresponding Redfield equation is capable of reproducing the characteristic features of the non-Markovian quantum behavior of the model.

Revisiting the naturalness problem: Who is afraid of quadratic divergences?

It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences---which can always be absorbed into a position of the critical surface---should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.

Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay

In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.

Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability

We study semiconductor ring lasers subject to delayed optical feedback from one or two short external cavities. In case of two cavities we consider the feedback strengths and phases to be either symmetric or asymmetric feedback. When feedback is symmetric, the laser operates in a bi-directional continuous wave or periodic regime for most parameter values. Only for some small parameter regions complex dynamics, such as quasi-periodicity and chaos are obtained. When the feedback is asymmetric complex dynamical regimes, including chaos, are obtained in large parameter regions. We explain complex dynamical regimes obtained in both symmetric and asymmetric feedback cases by linear stability of the stationary solutions calculated using DDE-BIFTOOL.

Leg-adjustment strategies for stable running in three dimensions

The dynamics of the center of mass (CoM) in the sagittal plane in humans and animals during running is well described by the spring-loaded inverted pendulum (SLIP). With appropriate parameters, SLIP running patterns are stable, and these models can recover from perturbations without the need for corrective strategies, such as the application of additional forces. Rather, it is sufficient to adjust the leg to a fixed angle relative to the ground. In this work, we consider the extension of the SLIP to three dimensions (3D SLIP) and investigate feed-forward strategies for leg adjustment during the flight phase. As in the SLIP model, the leg is placed at a fixed angle. We extend the scope of possible reference axes from only fixed horizontal and vertical axes to include the CoM velocity vector as a movement-related reference, resulting in six leg-adjustment strategies. Only leg-adjustment strategies that include the CoM velocity vector produced stable running and large parameter domains of stability. The ability of the model to recover from perturbations along the direction of motion (directional stability) depended on the strategy for lateral leg adjustment. Specifically, asymptotic and neutral directional stability was observed for strategies based on the global reference axis and the velocity vector, respectively. Additional features of velocity-based leg adjustment are running at arbitrary low speed (kinetic energy) and the emergence of large domains of stable 3D running that are smoothly transferred to 2D SLIP stability and even to 1D SLIP hopping. One of the additional leg-adjustment strategies represented a large convex region of parameters where stable and robust hopping and running patterns exist. Therefore, this strategy is a promising candidate for implementation into engineering applications, such as robots, for instance. In a preliminary comparison, the model predictions were in good agreement with the experimental data, suggesting that the 3D SLIP is an appropriate model to describe human running in three dimensions. The prediction of stable running based on movement-related leg-adjustment strategies indicates that both humans and robots may not require external targets directing the movement to run in three dimensions based on compliant leg function. This new movement-based reference enables the control of 3D running because leg adjustment is less sensitive and gait stability is separated from directional stability.

Density, spin, and pairing instabilities in polarized ultracold Fermi gases

We study the influence of population imbalance on the pairing, spin, and density instabilities of a two component ideal Fermi gas after a sudden quench of interactions near a Feshbach resonance. Over a large region of parameters the pairing instability is dominated by finite momentum pairing, suggesting the possibility of observing FFLO-like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the BCS side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the BEC side of the resonance, the pairing instability is present for scattering lengths that are larger than a critical value that is only weakly dependent on population imbalance and always smaller than the scattering length at which the Stoner-like spin instability occurs.

QUANTUM CAPACITY REGION OF SIMULTANEOUS AMPLITUDE AND PHASE DAMPED QUBIT CHANNEL

A typical channel model of the decoherence of qubit is the simultaneous amplitude and phase damping. The parameter region of the channel is classified using the degradability and anti-degradability. It is shown that there is a large parameter region with zero quantum capacity. The formula for one-shot quantum capacity is also given.

Controlling the quantum state of a single photon emitted from a single polariton

We investigate in detail the optimal conditions for a high fidelity transfer from a single-polariton state to a single-photon state and subsequent homodyne detection of the single photon. We assume that, using various possible techniques, the single polariton has initially been stored as a spin-wave grating in a cloud of cold atoms inside a low-finesse cavity. This state is then transferred to a single-photon optical pulse using an auxiliary beam. We optimize the retrieval efficiency and determine the mode of the local oscillator that maximizes the homodyne efficiency of such a photon. We find that both efficiencies can have values close to one in a large region of experimental parameters.

Phase diagram of theJ1−J2−J3Heisenberg model on the honeycomb lattice: A series expansion study

We study magnetically-ordered phases and their phase boundaries in the ${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ Heisenberg models on the honeycomb lattice using series expansions around N\'eel and different colinear and noncolinear magnetic states. An Ising anisotropy ($\ensuremath{\lambda}={J}_{\ensuremath{\perp}}/{J}_{z}\ensuremath{\ne}1$) is introduced and ground-state energy and magnetization order parameter are calculated as a power series expansion in $\ensuremath{\lambda}$. Series extrapolation methods are used to study properties for the Heisenberg model ($\ensuremath{\lambda}=1$). We find that at large ${J}_{3}$ ($>0.6$) there is a first-order transition between N\'eel and columnar states, in agreement with the classical answer. For ${J}_{3}=0$, we find that the N\'eel phase extends beyond the region of classical stability. We also find that spiral phases are stabilized over large parameter regions, although their spiral angles can be substantially renormalized with respect to the classical values. Our study also shows a magnetically disordered region at intermediate ${J}_{2}/{J}_{1}$ and ${J}_{3}/{J}_{1}$ values.

The survival of the conformist: Social pressure and renewable resource management

This paper examines the role of other-regarding behavior as a mechanism for the establishment and maintenance of cooperation in resource use under variable social and environmental conditions. By coupling resource stock dynamics with social dynamics concerning compliance to a social norm prescribing non-excessive resource extraction in a common pool resource, we show that when reputational considerations matter and a sufficient level of social stigma affects the violators of a norm, sustainable outcomes are achieved. We find large parameter regions where norm-observing and norm-violating types coexist, and analyze to what extent such coexistence depends on the environment.

Inflection point inflation: WMAP constraints and a solution to the fine tuning problem

We consider observational constraints and fine-tuning issues in a renormalizable model of inflection point inflation, with two independent parameters. We derive constraints on the parameter space of this model arising from the WMAP 7-year power spectrum. It has previously been shown that it is possible to successfully embed this potential in the MSSM. Unfortunately, to do this requires severe fine-tuning. We address this issue by introducing a hybrid field to dynamically uplift the potential with a subsequent smooth phase transition to end inflation at the necessary point. Large parameter regions exist where this drastically reduces the fine-tuning required without ruining the viability of the model. A side effect of this mechanism is that it increases the width of the slow-roll region of the potential, thus also alleviating the problem of the fine-tuning of initial conditions. The MSSM embedding we study has been previously shown to be able to explain the smallness of the neutrino masses. The hybrid transition does not spoil this feature as there exist parameter regions where the fine-tuning parameter is as large as 10−1 and the neutrino masses remain small.

A Model for Optimal Offspring Size in Fish, Including Live-Bearing and Parental Effects

Since Smith and Fretwell's seminal article in 1974 on the optimal offspring size, most theory has assumed a trade-off between offspring number and offspring fitness, where larger offspring have better survival or fitness, but with diminishing returns. In this article, we use two ubiquitous biological mechanisms to derive the shape of this trade-off: the offspring's growth rate combined with its size-dependent mortality (predation). For a large parameter region, we obtain the same sigmoid relationship between offspring size and offspring survival as Smith and Fretwell, but we also identify parameter regions where the optimal offspring size is as small or as large as possible. With increasing growth rate, the optimal offspring size is smaller. We then integrate our model with strategies of parental care. Egg guarding that reduces egg mortality favors smaller or larger offspring, depending on how mortality scales with size. For live-bearers, the survival of offspring to birth is a function of maternal survival; if the mother's survival increases with her size, then the model predicts that larger mothers should produce larger offspring. When using parameters for Trinidadian guppies Poecilia reticulata, differences in both growth and size-dependent predation are required to predict observed differences in offspring size between wild populations from high- and low-predation environments.

Anisotropic power-law inflation

We study an inflationary scenario in supergravity model with a gauge kinetic function.We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic functionare exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.