The connection between Bohmian mechanics and many-particle quantum hydrodynamics

Bohm developed the Bohmian mechanics (BM), in which the Schrödinger equation is transformed into two differential equations: a continuity equation and an equation of motion similar to the Newtonian equation of motion. This transformation can be executed both for single-particle systems and for many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum mechanics for the derivation of many-particle quantum hydrodynamics (MPQHD) including one differential equation for the mass balance and two differential equations for the momentum balance, and we extended their analysis in a prework (K. Renziehausen, I. Barth in Prog. Theor. Exp. Phys. 2018:013A05, 2018) for the case that the particle ensemble consists of different particle sorts. The purpose of this paper is to show how the differential equations of MPQHD can be derived for such a particle ensemble with the differential equations of BM as a starting point. Moreover, our discussion clarifies that the differential equations of MPQHD are more suitable for an analysis of many-particle systems than the differential equations of BM because the differential equations of MPQHD depend on a single position vector only while the differential equations of BM depend on the complete set of all particle coordinates

On the exact rotational and internal Hamiltonian for a non-relativistic closed many-body system

Without applying Born-Oppenheimer approximation, the non-relativistic Hamiltonian can be separated into Hamiltonians for the translation of the center of mass and for the rotational and internal motions of the closed many-body system. This exact rotational and internal Hamiltonian can be expressed in terms of three Euler angles for three independent rotations of the system and the rotated Jacobi coordinates for the internal motions

Many-particle quantum hydrodynamics: Exact equations and pressure tensors

In the first part of this paper, the many-particle quantum hydrodynamics equations for a system containing many particles of different sorts are derived exactly from the many-particle Schrödinger equation, including the derivation of the many-particle continuity equations, many-particle Ehrenfest equations of motion, and many-particle quantum Cauchy equations for any of the different particle sorts and for the total particle ensemble. The new point in our analysis is that we consider a set of arbitrary particles of different sorts in the system. In the many-particle quantum Cauchy equations, there appears a quantity called the pressure tensor. In the second part of this paper, we analyze two versions of this tensor in depth: the Wyatt pressure tensor and the Kuzmenkov pressure tensor. There are different versions because there is a gauge freedom for the pressure tensor similar to that for potentials. We find that the interpretation of all the quantities contributing to the Wyatt pressure tensor is understandable, but for the Kuzmenkov tensor it is difficult. Furthermore, the transformation from Cartesian coordinates to cylindrical coordinates for the Wyatt tensor can be done in a clear way, but for the Kuzmenkov tensor it is rather cumbersome

How to approximate the Dirac equation with the Mauser method

auser and coworkers discussed in a series of papers an ansatz how to split the Dirac equation and the wave function appearing therein into a part related to a free moving electron and another part related to a free moving positron. This ansatz includes an expansion of these quantities into orders of the reciprocal of the speed of light ϵ=1/c. In particular, in Mauser (VLSI Design 9:415, 1999) it is discussed how to apply this expansion up to the second order in the reciprocal of the speed of light ϵ. As an expansion of this analysis, we show in this work how all three well-known terms that appear in an expansion of the Dirac equation in second order on the reciprocal of the speed of light, namely, a relativistic correction to the kinetic energy, the Darwin term, and the spin-orbit interaction, can be found using the ansatz of Mauser—and doing so, we close a gap between this ansatz to approximate the Dirac equation and other approximative results found using the Foldy–Wouthuysen transformation

Time-dependent momentum expectation values from different quantum probability and flux densities

Based on the Ehrenfest theorem, the time-dependent expectation value of a momentum operator can be evaluated equivalently in two ways. The integrals appearing in the expressions are taken over two different functions. In one case, the integrand is the quantum mechanical flux density j̲ , and in the other, a different quantity j̃ ̲ appears, which also has the units of a flux density. The quantum flux density j̲ is related to the probability density ρ via the continuity equation, and j̃ ̲ may as well be used to define a density ρ̃ that fulfills a continuity equation. Employing a model for the coupled dynamics of an electron and a proton, we document the properties of the densities and flux densities. It is shown that although the mean momentum derived from the two quantities is identical, the various functions exhibit a very different coordinate and time-dependence. In particular, it is found that the flux density j̃ ̲ directly monitors temporal changes in the probability density, and the density ρ̃ carries information about wave packet dispersion occurring in different spatial directions

Deformation of Atomic p(+/-) Orbitals in Strong Elliptically Polarized Laser Fields: Ionization Time Drifts and Spatial Photoelectron Separation

We theoretically investigate the deformation of atomic p(+/-) orbitals driven by strong elliptically polarized (EP) laser fields and the role it plays in tunnel ionization. Our study reveals that different Stark effects induced by orthogonal components of the EP field give rise to subcycle rearrangement of the bound electron density, rendering the initial p(+) and p(-) orbitals deformed and polarized along distinctively tilted angles with respect to the polarization ellipse of the EP field. As a consequence, the instantaneous tunneling rates change such that for few-cycle EP laser pulses the bound electron initially counterrotating (corotating) with the electric field is most likely released before (after) the peak of the electric field. We demonstrate that with a sequential-pulse setup one can exploit this effect to spatially separate the photoelectrons detached from p(+) and p(-) orbitals, paving the way towards robust control of spin-resolved photoemission in laser-matter interactions

Efficacy of arginine depletion by ADI-PEG20 in an intracranial model of GBM

Glioblastoma multiforme (GBM) remains a cancer with a poor prognosis and few effective therapeutic options. Successful medical management of GBM is limited by the restricted access of drugs to the central nervous system (CNS) caused by the blood brain barrier (BBB). We previously showed that a subset of GBM are arginine auxotrophic because of transcriptional silencing of ASS1 and/or ASL and are sensitive to pegylated arginine deiminase (ADI-PEG20). However, it is unknown whether depletion of arginine in peripheral blood in vivo has therapeutic activity against intracranial disease. In the present work, we describe the efficacy of ADI-PEG20 in an intracranial model of human GBM in which tumour growth and regression are assessed in real time by measurement of luciferase activity. Animals bearing intracranial human GBM tumours of varying ASS status were treated with ADI-PEG20 alone or in combination with temozolomide and monitored for tumour growth and regression. Monotherapy ADI-PEG20 significantly reduces the intracranial growth of ASS1 negative GBM and extends survival of mice carrying ASS1 negative GBM without obvious toxicity. The combination of ADI-PEG20 with temozolomide (TMZ) demonstrates enhanced effects in both ASS1 negative and ASS1 positive backgrounds.Our data provide proof of principle for a therapeutic strategy for GBM using peripheral blood arginine depletion that does not require BBB passage of drug and is well tolerated. The ability of ADI-PEG20 to cytoreduce GBM and enhance the effects of temozolomide argues strongly for its early clinical evaluation in the treatment of GBM

Encapsulation of temozolomide in a calixarene nanocapsule improves its stability and enhances its therapeutic efficacy against glioblastoma

The alkylating agent temozolomide (TMZ) is the first-line chemotherapeutic for glioblastoma (GBM), a common and aggressive primary brain tumour in adults. However, its poor stability and unfavourable pharmacokinetic profile limit its clinical efficacy. There is an unmet need to tailor the therapeutic window of TMZ, either through complex derivatization or by utilizing pharmaceutical excipients. To enhance stability and aqueous solubility, we encapsulated TMZ in a p-sulphonatocalix[4]arene (Calix) nanocapsule and employed 1H-NMR, LC-MS and UV-Vis spectroscopy to chart the stability of this novel TMZ@Calix complex according to FDA and EMA guidelines. LC-MS/MS plasma stability assays were conducted in mice to further explore the stability profile of TMZ@Calix in vivo. The therapeutic efficacy of TMZ@Calix was compared to that of unbound TMZ in GBM cell lines and patient derived primary cells with known O6-methylguanine-DNA methyltransferase (MGMT) expression status and in vivo in an intracranial U87 xenograft mouse model. Encapsulation significantly enhanced the stability of TMZ in all conditions tested. TMZ@Calix was more potent than native TMZ at inhibiting the growth of established GBM cell lines and patient derived primary lines expressing MGMT and highly resistant to TMZ. In vivo, native TMZ was rapidly degraded in mouse plasma, whereas the stability of TMZ@Calix was enhanced 3-fold with increased therapeutic efficacy in an orthotopic model. In the absence of new effective therapies, this novel formulation is of clinical importance serving as an inexpensive and highly efficient treatment that could be made readily available to GBM patients and warrants further pre-clinical and clinical evaluation