Presence Of Local Perturbations Research Articles

Fermion parity gap and exponential ground state degeneracy of the one-dimensional Fermi gas with intrinsic attractive interaction

We examine the properties of a one-dimensional (1D) Fermi gas with attractive intrinsic (Hubbard) interactions in the presence of spin-orbit coupling and Zeeman field by numerically computing the pair binding energy, excitation gap, and susceptibility to local perturbations using the density matrix renormalization group. Such a system can, in principle, be realized in a system of ultracold atoms confined in a 1D optical lattice. We note that, in the presence of spatial interfaces introduced by a smooth parabolic potential, the pair binding and excitation energy of the system decays exponentially with the system size, pointing to the existence of an exponential ground state degeneracy, and is consistent with recent works. However, the susceptibility of the ground state degeneracy of this number-conserving system to local impurities indicates that the energy gap vanishes as a power law with the system size in the presence of local perturbations. We compare this system with the more familiar system of an Ising antiferromagnet in the presence of a transverse field realized with Rydberg atoms and argue that the exponential splitting in the clean number-conserving 1D Fermi system is similar to a phase with only conventional order.

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene, conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature. For this reason, the bounding of electrons in graphene in the form of geometries of quantum dots is impossible. In gapless graphene, due to its unique electronic band structure, there is a minimal conductivity at Dirac points, that is, in the limit of zero doping. This creates a problem for using such a highly motivated new material in electronic devices. One of the ways to overcome this problem is the creation of a band gap in the graphene band structure, which is made by inversion symmetry breaking (symmetry of sublattices). We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for “local chemical potential” and “local gap”. The calculated energy spectrum exhibits quite different features with and without the perturbations. A characteristic equation for bound states (BSs) has been obtained. It is surprisingly found that the relation between the radial functions of sublattices wave functions, i.e., , , and , , can be established by SO(2) group.

Numerical analysis for a molten salt reactor in the presence of localized perturbations

Molten salt reactors (MSRs) have seen a marked resurgence of interest over the past few decades, highlighted by their inclusion as one of the six Generation IV reactor types. The MSRs are characterized by using the fluid-fuel, so that their technologies are fundamentally different from those used in the conventional solid-fuel reactors. In this paper, the attention is focused on the behaviors of an MSR in the presence of localized perturbations caused by fissile precipitates and gas bubbles. A neutron kinetic model considering the fuel salt flow is established based on the neutron diffusion theory, which consists of two-group neutron diffusion equations for the fast and thermal neutron fluxes and six-group balance equations for delayed neutron precursors, and the group constants dependent on the temperature are calculated by the code DRAGON. In addition, the k-epsilon turbulent model is adopted to establish the flow and heat transfer. The thermo-hydraulic and neutronic models are coupled through the temperature, heat source and velocity. The effects of the localized perturbation on the distributions of power, temperature, neutron fluxes and delayed neutron precursors are obtained and discussed in detail. The results provide some valuable information for the research and design of this new generation reactor.

Breakdown of a perturbed topological phase

We studied the robustness of a generalized Kitaev's toric code with degrees of freedom in the presence of local perturbations. For N = 2, this model reduces to the conventional toric code in a uniform magnetic field. A quantitative analysis was performed for the perturbed toric code by applying a combination of high-order series expansions and variational techniques. We found strong evidence for first- and second-order phase transitions between topologically ordered and polarized phases. Most interestingly, our results also indicate the existence of topological multi-critical points in the phase diagram.

Fluorescence lifetimes and predissociation processes in the B̃ 2A′ state of CCH

Fluorescence lifetimes have been measured under supersonic jet conditions for various N, K-rotational levels of three vibrational levels (T, T+ν2, and T+ν3) of the B̃ 2A′ state of CCH. It was found that the lifetimes of levels T+ν2 and T+ν3 are significantly shorter than that of level T. Furthermore, the lifetimes vary in a complicated way from one rovibronic level to another, indicating the presence of local perturbations. The previously reported CC–H bond energy ranges from 95.6 to 116.3 kcal/mol, which leads to a large uncertainty in assigning the onset of the dissociation process, CCH (X̃ 2Σ+)→C2(X 1Σg+)+H(2S1/2). In this work, fluorescence excitation spectra of photofragment C2 via D 1Σu+←X 1Σg+ and d 3Πg←a 3Πu have been recorded to determine the predissociation processes of the B̃ state. Assuming no barrier is present in the dissociation process of the X̃ and à states, the upper bound of D00(CC–H) was estimated as 39 388±7 cm−1(≃112.62 kcal/mol). Hence, the lifetime quenching phenomenon observed in the B̃ state is primarily due to predissociation via the dissociative continuum of either the X̃ or the à state of CCH.

New approach to the x-ray-absorption problem

We present a simple numerically stable procedure for calculating frequency-dependent response functions for a fermion system in the presence of localized perturbations over all frequency scales. In the case of the x-ray singularity problem, the asymptotic result of Nozieres and De Dominicis can be extended to excitation energies comparable to the bandwidth. The range of this extension depends on the structure of the localized perturbation.