Distributional Borel Summability of Odd Anharmonic Oscillators

It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances naturally associated with the system

Perturbation theory of PT-symmetric Hamiltonians

In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of \PTsymmetric Hamiltonians is proved using stability techniques. We apply this method to \PTsymmetric unperturbed Hamiltonians perturbed by \PTsymmetric additional interactions

Canonical Expansion of PT-Symmetric Operators and Perturbation Theory

Let $H$ be any \PT symmetric Schr\"odinger operator of the type $-\hbar^2\Delta+(x_1^2+...+x_d^2)+igW(x_1,...,x_d)$ on $L^2(\R^d)$, where $W$ is any odd homogeneous polynomial and $g\in\R$. It is proved that $\P H$ is self-adjoint and that its eigenvalues coincide (up to a sign) with the singular values of $H$, i.e. the eigenvalues of $\sqrt{H^\ast H}$. Moreover we explicitly construct the canonical expansion of $H$ and determine the singular values $\mu_j$ of $H$ through the Borel summability of their divergent perturbation theory. The singular values yield estimates of the location of the eigenvalues \l_j of $H$ by Weyl's inequalities.Comment: 20 page

Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant

Comparison between the exact value of the spectral zeta function, $Z_{H}(1)=5^{-6/5}[3-2\cos(\pi/5)]\Gamma^2(1/5)/\Gamma(3/5)$, and the results of numeric and WKB calculations supports the conjecture by Bessis that all the eigenvalues of this PT-invariant hamiltonian are real. For one-dimensional Schr\"odinger operators with complex potentials having a monotonic imaginary part, the eigenfunctions (and the imaginary parts of their logarithmic derivatives) have no real zeros.Comment: 6 pages, submitted to J. Phys.

Scalar Quantum Field Theory with Cubic Interaction

In this paper it is shown that an i phi^3 field theory is a physically acceptable field theory model (the spectrum is positive and the theory is unitary). The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.Comment: Corrected expressions in equations (20) and (21

PTPT symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum

Consider in $L^2(R^d)$, $d\geq 1$, the operator family $H(g):=H_0+igW$. \ds H_0= a^\ast_1a_1+... +a^\ast_da_d+d/2 is the quantum harmonic oscillator with rational frequencies, $W$ a $P$ symmetric bounded potential, and $g$ a real coupling constant. We show that if $|g|<\rho$, $\rho$ being an explicitly determined constant, the spectrum of $H(g)$ is real and discrete. Moreover we show that the operator \ds H(g)=a^\ast_1 a_1+a^\ast_2a_2+ig a^\ast_2a_1 has real discrete spectrum but is not diagonalizable.Comment: 20 page

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

Thermodynamics of Pseudo-Hermitian Systems in Equilibrium

In study of pseudo(quasi)-hermitian operators, the key role is played by the positive-definite metric operator. It enables physical interpretation of the considered systems. In the article, we study the pseudo-hermitian systems with constant number of particles in equilibrium. We show that the explicit knowledge of the metric operator is not essential for study of thermodynamic properties of the system. We introduce a simple example where the physically relevant quantities are derived without explicit calculation of either metric operator or spectrum of the Hamiltonian.Comment: 9 pages, 2 figures, to appear in Mod.Phys.Lett. A; historical part of sec. 2.1 reformulated, references corrected; typos correcte

Recent Advances in Understanding the Protein Corona of Nanoparticles and in the Formulation of “Stealthy” Nanomaterials

In the last decades, the staggering progress in nanotechnology brought around a wide and heterogeneous range of nanoparticle-based platforms for the diagnosis and treatment of many diseases. Most of these systems are designed to be administered intravenously. This administration route allows the nanoparticles (NPs) to widely distribute in the body and reach deep organs without invasive techniques. When these nanovectors encounter the biological environment of systemic circulation, a dynamic interplay occurs between the circulating proteins and the NPs, themselves. The set of proteins that bind to the NP surface is referred to as the protein corona (PC). PC has a critical role in making the particles easily recognized by the innate immune system, causing their quick clearance by phagocytic cells located in organs such as the lungs, liver, and spleen. For the same reason, PC defines the immunogenicity of NPs by priming the immune response to them and, ultimately, their immunological toxicity. Furthermore, the protein corona can cause the physical destabilization and agglomeration of particles. These problems induced to consider the PC only as a biological barrier to overcome in order to achieve efficient NP-based targeting. This review will discuss the latest advances in the characterization of PC, development of stealthy NP formulations, as well as the manipulation and employment of PC as an alternative resource for prolonging NP half-life, as well as its use in diagnostic applications