Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].Comment: 22 pages, 13 figures. Added references, minor revision

Excited state g-functions from the Truncated Conformal Space

In this paper we consider excited state g-functions, that is, overlaps between boundary states and excited states in boundary conformal field theory. We find a new method to calculate these overlaps numerically using a variation of the truncated conformal space approach. We apply this method to the Lee-Yang model for which the unique boundary perturbation is integrable and for which the TBA system describing the boundary overlaps is known. Using the truncated conformal space approach we obtain numerical results for the ground state and the first three excited states which are in excellent agreement with the TBA results. As a special case we can calculate the standard g-function which is the overlap with the ground state and find that our new method is considerably more accurate than the original method employed by Dorey et al.Comment: 21 pages, 6 figure

Quantum counterpart of spontaneously broken classical PT symmetry

The classical trajectories of a particle governed by the PT-symmetric Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) have been studied in depth. It is known that almost all trajectories that begin at a classical turning point oscillate periodically between this turning point and the corresponding PT-symmetric turning point. It is also known that there are regions in $\epsilon$ for which the periods of these orbits vary rapidly as functions of $\epsilon$ and that in these regions there are isolated values of $\epsilon$ for which the classical trajectories exhibit spontaneously broken PT symmetry. The current paper examines the corresponding quantum-mechanical systems. The eigenvalues of these quantum systems exhibit characteristic behaviors that are correlated with those of the associated classical system.Comment: 11 pages, 7 figure

Factors influencing the potency of marbofloxacin for pig pneumonia pathogens Actinobacillus pleuropneumoniae and Pasteurella multocida

For the pig respiratory tract pathogens, Actinobacillus pleuropneumoniae and Pasteurella multocida, Minimum Inhibitory Concentration (MIC) of marbofloxacin was determined in recommended broths and pig serum at three inoculum strengths. MICs in both growth matrices increased progressively from low, through medium to high starting inoculum counts, 104, 106 and 108 CFU/mL, respectively. P. multocida MIC ratios for high:low inocula were 14:4:1 for broth and 28.2:1 for serum. Corresponding MIC ratios for A. pleuropneumoniae were lower, 4.1:1 (broth) and 9.2:1 (serum). MIC high:low ratios were therefore both growth matrix and bacterial species dependent. The effect of alterations to the chemical composition of broths and serum on MIC were also investigated. Neither adjusting broth or serum pH in six increments over the range 7.0 to 8.0 nor increasing calcium and magnesium concentrations of broth in seven incremental steps significantly affected MICs for either organism. In time-kill studies, the killing action of marbofloxacin had the characteristics of concentration dependency against both organisms in both growth matrices. It is concluded that MIC and time-kill data for marbofloxacin, generated in serum, might be preferable to broth data, for predicting dosages of marbofloxacin for clinical use

All Hermitian Hamiltonians Have Parity

It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an eigenstate of P with eigenvalue (-1)^n. Given these properties, it is appropriate to refer to P as the parity operator and to say that H has parity symmetry, even though P may not refer to spatial reflection. Thus, if the Hamiltonian has the form H=p^2+V(x), where V(x) is real (so that H possesses time-reversal symmetry), then it immediately follows that H has PT symmetry. This shows that PT symmetry is a generalization of Hermiticity: All Hermitian Hamiltonians of the form H=p^2+V(x) have PT symmetry, but not all PT-symmetric Hamiltonians of this form are Hermitian

Potency of marbofloxacin for pig pneumonia pathogens Actinobacillus pleuropneumoniae and Pasteurella multocida: Comparison of growth media

Pharmacodynamic properties of marbofloxacin were established for six isolates each of the pig respiratory tract pathogens, Actinobacillus pleuropneumoniae and Pasteurella multocida. Three in vitro indices of potency were determined; Minimum Inhibitory Concentration (MIC), Minimum Bactericidal Concentration (MBC) and Mutant Prevention Concentration (MPC). For MIC determination Clinical Laboratory Standards Institute guidelines were modified in three respects: (1) comparison was made between two growth media, an artificial broth and pig serum; (2) a high inoculum count was used to simulate heavy clinical bacteriological loads; and (3) five overlapping sets of two-fold dilutions were used to improve accuracy of determinations. Similar methods were used for MBC and MPC estimations. MIC and MPC serum:broth ratios for A. pleuropneumoniae were 0.79:1 and 0.99:1, respectively, and corresponding values for P. multocida were 1.12:1 and 1.32:1. Serum protein binding of marbofloxacin was 49%, so that fraction unbound (fu) serum MIC values were significantly lower than those predicted by correction for protein binding; fu serum:broth MIC ratios were 0.40:1 (A. pleuropneumoniae) and 0.50:1 (P. multocida). For broth, MPC:MIC ratios were 13.7:1 (A. pleuropneumoniae) and 14.2:1 (P. multocida). Corresponding ratios for serum were similar, 17.2:1 and 18.8:1, respectively. It is suggested that, for dose prediction purposes, serum data might be preferable to potency indices measured in broths

On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references adde

On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts

In the context of two particularly interesting non-Hermitian models in quantum mechanics we explore the relationship between the original Hamiltonian H and its Hermitian counterpart h, obtained from H by a similarity transformation, as pointed out by Mostafazadeh. In the first model, due to Swanson, h turns out to be just a scaled harmonic oscillator, which explains the form of its spectrum. However, the transformation is not unique, which also means that the observables of the original theory are not uniquely determined by H alone. The second model we consider is the original PT-invariant Hamiltonian, with potential V=igx^3. In this case the corresponding h, which we are only able to construct in perturbation theory, corresponds to a complicated velocity-dependent potential. We again explore the relationship between the canonical variables x and p and the observables X and P.Comment: 9 pages, no figure