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We consider a macroscopic quantum system with unitarily evolving pure state $\psi_t\in \mathcal{H}$ and take it for granted that different macro states correspond to mutually orthogonal, high-dimensional subspaces $\mathcal{H}_\nu$ (macro spaces) of $\mathcal{H}$. Let $P_\nu$ denote the projection to $\mathcal{H}_\nu$. We prove two facts about the evolution of the superposition weights $\|P_\nu\psi_t\|^2$: First, given any $T>0$, for most initial states $\psi_0$ from any particular macro space $\mathcal{H}_\mu$ (possibly far from thermal equilibrium), the curve $t\mapsto \|P_\nu \psi_t\|^2$ is approximately the same (i.e., nearly independent of $\psi_0$) on the time interval $[0,T]$. And second, for most $\psi_0$ from $\mathcal{H}_\mu$ and most $t\in[0,\infty)$, $\|P_\nu \psi_t\|^2$ is close to a value $M_{\mu\nu}$ that is independent of both $t$ and $\psi_0$. The first is an instance of the phenomenon of dynamical typicality observed by Bartsch, Gemmer, and Reimann, and the second modifies, extends, and in a way simplifies the concept, introduced by von Neumann, now known as normal typicality., Comment: 28 pages LaTeX, 3 figures

Agonists and antagonists of the canonical Wnt signaling pathway are modulators of pathological aspects of rheumatoid arthritis (RA). Their activity is primarily modifying bone loss and bone formation, as shown in animal models of RA. More recently, modulation of Wnt signaling by the antagonist Sclerostin has also been shown to influence soft-tissue-associated inflammatory aspects of the disease pointing towards a role of Wnt signaling in soft-tissue inflammation as well. Yet, nothing is known experimentally about the role of Wnt ligands in RA. Here we provide evidence that altering Wnt signaling at the level of a ligand affects all aspects of the rheumatoid arthritic disease. WNT9a levels are increased in the pannus tissue of RA patients, and stimulation of synovial fibroblasts (SFB) with tumor necrosis factor (TNF) leads to increased transcription of Wnt9a. Loss of Wnt9a in a chronic TNF-dependent RA mouse model results in an aggravation of disease progression with enhanced pannus formation and joint destruction. Yet, loss of its activity in the acute K/BxN serum-transfer induced arthritis (STIA) mouse model, which is independent of TNF signaling, has no effect on disease severity or progression. Thus, suggesting a specific role for WNT9a in TNF-triggered RA. In synovial fibroblasts, WNT9a can activate the canonical Wnt/β-catenin pathway, but it can also activate P38- and downregulate NFκB signaling. Based on in vitro data, we propose that loss of Wnt9a creates a slight proinflammatory and procatabolic environment that boosts the TNF-mediated inflammatory response.

Scoliosis is an abnormal bending of the body axis. Truncated vertebrae or a debilitated ability to control the musculature in the back can cause this condition, but in most cases the causative reason for scoliosis is unknown (idiopathic). Using mutants for somite clock genes with mild defects in the vertebral column, we here show that early defects in somitogenesis are not overcome during development and have long lasting and profound consequences for muscle fiber organization, structure and whole muscle volume. These mutants present only mild alterations in the vertebral column, and muscle shortcomings are uncoupled from skeletal defects. None of the mutants presents an overt musculoskeletal phenotype at larval or early adult stages, presumably due to compensatory growth mechanisms. Scoliosis becomes only apparent during aging. We conclude that adult degenerative scoliosis is due to disturbed crosstalk between vertebrae and muscles during early development, resulting in subsequent adult muscle weakness and bending of the body axis.

Osteoarthritis (OA) is a common degenerative disease of the joint, with a complex multifactorial not yet fully understood etiology. Over the past years, the Wnt signaling pathway has been implicated in osteoarthritis. In a recent genomewide association study (GWAS), the chromosomal location on chromosome 1, linked to the Wnt3a-Wnt9a gene locus, was identified as the most significant locus associated with a thumb osteoarthritis endophenotype. Previously, it was shown that WNT9a is involved in maintaining synovial cell identity in the elbow joint during embryogenesis. Here, we report that the conditional loss of Wnt9a in the Prx1-Cre expressing limb mesenchyme or Prg4-CreER expressing cells predispositions the mice to develop spontaneous OA-like changes with age. In addition, the trabecular bone volume is altered in these mice. Similarly, mice with a conditional loss of Wnt4 in the limb mesenchyme are also more prone to develop spontaneously OA-like joint alterations with age. These mice display additional alterations in their cortical bone. The combined loss of Wnt9a and Wnt4 increased the likelihood of the mice developing osteoarthritis-like changes and enhanced disease severity in the affected mice. © 2022 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the Hofstadter model on the Ammann-Beenker tiling of the plane has spectral gaps at certain energies, and we are able to prove the existence of a spectral gap where previous numerical results were inconclusive. Our algorithm is applicable to more general systems with finite local complexity and eventually finds all gaps, circumventing an earlier no-go theorem regarding the computability of spectral gaps for general Hamiltonians., Comment: paper + supplemental material

Based on a result by Yarotsky (J. Stat. Phys. 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences., 9 pages, 2 figures; v1->v2: added references, v2->v3: updated references

We first review the problem of a rigorous justification of Kubo's formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo's formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit., Contribution to the proceedings of QMath14 in Aarhus 2019

We consider the dynamics of $N$ interacting bosons initially forming a Bose-Einstein condensate. Due to an external trapping potential, the bosons are strongly confined in two dimensions, where the transverse extension of the trap is of order $\varepsilon$. The non-negative interaction potential is scaled such that its range and its scattering length are both of order $(N/\varepsilon^2)^{-1}$, corresponding to the Gross-Pitaevskii scaling of a dilute Bose gas. We show that in the simultaneous limit $N\rightarrow\infty$ and $\varepsilon\rightarrow 0$, the dynamics preserve condensation and the time evolution is asymptotically described by a Gross-Pitaevskii equation in one dimension. The strength of the nonlinearity is given by the scattering length of the unscaled interaction, multiplied with a factor depending on the shape of the confining potential. For our analysis, we adapt a method by Pickl to the problem with dimensional reduction and rely on the derivation of the one-dimensional NLS equation for interactions with softer scaling behaviour., Comment: v3:This version is to appear in Annales Henri Poincare; v2:Gap in the argument closed; improved presentation of the results

We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator $H_0$ does not commute with the spin operator in view of Rashba interactions, as in the typical models for the Quantum Spin Hall effect. A gapped periodic one-particle Hamiltonian $H_0$ is perturbed by adding a constant electric field of intensity $\varepsilon \ll 1$ in the $j$-th direction, and the linear response in terms of a $S$-current in the $i$-th direction is computed, where $S$ is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (Unit Cell Consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper $S$-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic $S$-current as the trace per unit volume of the $S$-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models., Comment: 49 pages, no figures. Keywords: quantum transport theory, spin conductivity, spin conductance, topological insulators, Spin Chern number

We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem holds also for certain perturbations of gapped ground states that close the spectral gap (so it is an adiabatic theorem also for resonances and in this sense `generalised'), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called `super-adiabatic'). In addition to existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations also for infinite systems. While we consider the result and its proof as new and interesting in itself, they also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article., Comment: V1 -> V2: improved presentation and additional references

The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized up to $\mathcal{O}(\varepsilon^{n+1})$ through a unitary transformation of the electronic subspace and the corresponding $n$th-order effective Hamiltonian is derived for the quantum nuclear motion. Explicit but general formulae are given for the second- and the third-order corrections. As a special case, the second-order Hamiltonian corresponding to an isolated electronic state is recovered which contains the coordinate-dependent mass-correction terms in the nuclear kinetic energy operator. For a multi-dimensional, explicitly coupled electronic band, the second-order Hamiltonian contains the usual BO terms and non-adiabatic corrections but generalized mass-correction terms appear as well. These, earlier neglected terms, perturbatively account for the outlying (discrete and continuous) electronic states not included in the explicitly coupled electronic subspace.

As the vertebrate skeleton develops it progresses from a solely cartilaginous scaffold to a mineralized bony skeleton. The cells that build up the skeleton, the chondrocytes and osteoblasts, are primarily of mesodermal origin. Yet, some facial bones, as well as the endocranium, are derived from neural crest cells. The differentiation of the mesenchymal cells to skeletal precursors as well as their subsequent differentiation and maturation along the two lineages, chondrogenic and osteogenic, is controlled by various different signaling pathways, among them Wnt-signaling. WNTs comprise a family of 19 secreted cysteine-rich glycoproteins and can signal through a variety of different intracellular pathways. Genetic loss- and gain-of-function experiments of Wnt-signaling pathway genes have helped to uncover their multiple roles in skeletogenesis, which will be discussed in this article primarily focusing on endochondral bone formation.

As the vertebrate skeleton develops it progresses from a solely cartilaginous scaffold to a mineralized bony skeleton. The cells that build up the skeleton, the chondrocytes and osteoblasts, are primarily of mesodermal origin. Yet, some facial bones, as well as the endocranium, are derived from neural crest cells. The differentiation of the mesenchymal cells to skeletal precursors as well as their subsequent differentiation and maturation along the two lineages, chondrogenic and osteogenic, is controlled by various different signaling pathways, among them Wnt-signaling. WNTs comprise a family of 19 secreted cysteine-rich glycoproteins and can signal through a variety of different intracellular pathways. Genetic loss- and gain-of-function experiments of Wnt-signaling pathway genes have helped to uncover their multiple roles in skeletogenesis, which will be discussed in this article primarily focusing on endochondral bone formation.

We are dealing with boundary conditions for Dirac-type operators, i.e., first order differential operators with matrix-valued coefficients, including in particular physical many-body Dirac operators. We characterize (what we conjecture is) the general form of reflecting boundary conditions (which includes known boundary conditions such as the one of the MIT bag model) and, as our main goal, of interior-boundary conditions (IBCs). IBCs are a new approach to defining UV-regular Hamiltonians for quantum field theories without smearing particles out or discretizing space. For obtaining such Hamiltonians, the method of IBCs provides an alternative to renormalization and has been successfully used so far in non-relativistic models, where it could be applied also in cases in which no renormalization method was known. A natural next question about IBCs is how to set them up for the Dirac equation, and here we take first steps towards the answer. For quantum field theories, the relevant boundary consists of the surfaces in $n$-particle configuration space $\mathbb{R}^{3n}$ on which two particles have the same location in $\mathbb{R}^3$. While this boundary has codimension 3, we focus here on the more basic situation in which the boundary has codimension 1 in configuration space. We describe specific examples of IBCs for the Dirac equation, we prove for some of these examples that they rigorously define self-adjoint Hamiltonians, and we develop the general form of IBCs for Dirac-type operators., 33 pages LaTeX, no figures; v2: Section 2.4 and Appendix A added

Recently, there has been progress in developing interior-boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while treating space as a continuum and electrons as point particles. An IBC can be expressed in the particle-position representation of a Fock vector $\psi$ as a condition on the values of $\psi$ on the set of collision configurations, and the corresponding Hamiltonian is defined on a domain of vectors satisfying this condition. We describe here how Bohmian mechanics can be extended to this type of Hamiltonian. In fact, part of the development of IBCs was inspired by the Bohmian picture. Particle creation and annihilation correspond to jumps in configuration space; the annihilation is deterministic and occurs when two particles (of the appropriate species) meet, whereas the creation is stochastic and occurs at a rate dictated by the demand for the equivariance of the $|\psi|^2$ distribution, time reversal symmetry, and the Markov property. The process is closely related to processes known as Bell-type quantum field theories., Comment: 50 pages LaTeX, 9 figures

Wnt signaling is important for proper embryonic development, shaping cell fate and migration, stem cell renewal, and organ and tissue formation. Here, Luther et al. investigated the role of Wnt1 in osteoporosis. Patients with early-onset osteoporosis and with WNT1 mutations had low bone turnover and high fracture rates, and loss of Wnt1 activity caused fracture and osteoporosis in mice. Inducing Wnt1 in bone-forming cells increased bone mass in aged mice, and this process did not require Lrp5, a co-receptor involved in Wnt signaling. This study identifies Wnt1 as an anabolic (bone building) factor and suggests that it might be a therapeutic target for osteoporosis.WNT1 mutations in humans are associated with a new form of osteogenesis imperfecta and with early-onset osteoporosis, suggesting a key role of WNT1 in bone mass regulation. However, the general mode of action and the therapeutic potential of Wnt1 in clinically relevant situations such as aging remain to be established. Here, we report the high prevalence of heterozygous WNT1 mutations in patients with early-onset osteoporosis. We show that inactivation of Wnt1 in osteoblasts causes severe osteoporosis and spontaneous bone fractures in mice. In contrast, conditional Wnt1 expression in osteoblasts promoted rapid bone mass increase in developing young, adult, and aged mice by rapidly increasing osteoblast numbers and function. Contrary to current mechanistic models, loss of Lrp5, the co-receptor thought to transmit extracellular WNT signals during bone mass regulation, did not reduce the bone-anabolic effect of Wnt1, providing direct evidence that Wnt1 function does not require the LRP5 co-receptor. The identification of Wnt1 as a regulator of bone formation and remodeling provides the basis for development of Wnt1-targeting drugs for the treatment of osteoporosis.

Immune cells regulate a hypertonic microenvironment in the skin; however, the biological advantage of increased skin Na(+) concentrations is unknown. We found that Na(+) accumulated at the site of bacterial skin infections in humans and in mice. We used the protozoan parasite Leishmania major as a model of skin-prone macrophage infection to test the hypothesis that skin-Na(+) storage facilitates antimicrobial host defense. Activation of macrophages in the presence of high NaCl concentrations modified epigenetic markers and enhanced p38 mitogen-activated protein kinase (p38/MAPK)-dependent nuclear factor of activated T cells 5 (NFAT5) activation. This high-salt response resulted in elevated type-2 nitric oxide synthase (Nos2)-dependent NO production and improved Leishmania major control. Finally, we found that increasing Na(+) content in the skin by a high-salt diet boosted activation of macrophages in a Nfat5-dependent manner and promoted cutaneous antimicrobial defense. We suggest that the hypertonic microenvironment could serve as a barrier to infection.

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC., Comment: 41 pages

International audience; We study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians that allow, in particular, for a detailed spectral analysis of magnetic waveguide Hamiltonians. We apply our general construction to a number of explicit examples, most of which are not covered by previous results.

We prove the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice. As an essential innovation, our result requires the spectral gap assumption only for the unperturbed Hamiltonian and applies to a large class of perturbations that close the spectral gap. Moreover, we prove formulas also for higher order response coefficients. Our justification of linear response theory is based on a novel extension of the adiabatic theorem to situations where a time-dependent perturbation closes the gap. According to the standard version of the adiabatic theorem, when the perturbation is switched on adiabatically and as long as the gap does not close, the initial ground state evolves into the ground state of the perturbed operator. The new adiabatic theorem states that for perturbations that are either slowly varying potentials or small quasi-local operators, once the perturbation closes the gap, the adiabatic evolution follows non-equilibrium almost-stationary states (NEASS) that we construct explicitly., v1->v2 section 4 on linear response added, presentation partly reworked. v2->v3 slightly stronger statements for "fast" switching. Final version as to appear in CMP

We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the size of the system. Our result provides an adiabatic expansion to all orders, in particular, also for initial data that lie in eigenspaces of degenerate eigenvalues. Our proof is based on ideas from a recent work of Bachmann et al. who proved an adiabatic theorem for interacting spin systems. As one important application of this adiabatic theorem, we provide the first rigorous derivation of the so-called linear response formula for the current density induced by an adiabatic change of the Hamiltonian of a system of interacting fermions in a ground state, with error estimates uniform in the system size. We also discuss the application to quantum Hall systems., 46 pages; v1->v2: typos corrected, references added, Remark 4 after Thm 2 slightly reworded, v2->v3: major revision of the presentation of the result, 3 figures added

We provide a constructive proof of exponentially localized Wannier functions and related Bloch frames in 1- and 2-dimensional time-reversal symmetric (TRS) topological insulators. The construction is formulated in terms of periodic TRS families of projectors (corresponding, in applications, to the eigenprojectors on an arbitrary number of relevant energy bands), and is thus model-independent. The possibility to enforce also a TRS constraint on the frame is investigated. This leads to a topological obstruction in dimension 2, related to $\mathbb{Z}_2$ topological phases. We review several proposals for $\mathbb{Z}_2$ indices that distinguish these topological phases, including the ones by Fu--Kane [Phys. Rev. B 74 (2006), 195312], Prodan [Phys. Rev. B 83 (2011), 235115], Graf--Porta [Commun. Math. Phys. 324 (2013), 851] and Fiorenza--Monaco--Panati [Commun. Math. Phys., in press]. We show that all these formulations are equivalent. In particular, this allows to prove a geometric formula for the the $\mathbb{Z}_2$ invariant of 2-dimensional TRS topological insulators, originally indicated in [Phys. Rev. B 74 (2006), 195312], which expresses it in terms of the Berry connection and the Berry curvature., Comment: 54 pages, 5 figures. Minor changes with respect to v1, including an updated bibliography. This version is published in Rev. Math. Phys

We investigate the localization properties of independent electrons in a periodic background, possibly including a periodic magnetic field, as e.g. in Chern insulators and in Quantum Hall systems. Since, generically, the spectrum of the Hamiltonian is absolutely continuous, localization is characterized by the decay, as $|x| \rightarrow \infty$, of the composite (magnetic) Wannier functions associated to the Bloch bands below the Fermi energy, which is supposed to be in a spectral gap. We prove the validity of a localization dichotomy, in the following sense: either there exist exponentially localized composite Wannier functions, and correspondingly the system is in a trivial topological phase with vanishing Hall conductivity, or the decay of any composite Wannier function is such that the expectation value of the squared position operator, or equivalently of the Marzari-Vanderbilt localization functional, is $+ \infty$. In the latter case, the Bloch bundle is topologically non-trivial, and one expects a non-zero Hall conductivity., 45 pages, 2 figures

Formulas for the contribution of the conduction electrons to the polarization and magnetization are derived for disordered systems and within a one-particle framework. These results generalize known formulas for Bloch electrons and the presented proofs considerably simplify and strengthen prior justifications. The new formulas show that orbital polarization and magnetization are of geometric nature. This leads to quantization for a periodically driven Piezo effect as well as the derivative of the magnetization w.r.t. the chemical potential. It is also shown how the latter is connected to boundary currents in Chern insulators. The main technical tools in the proofs are an adaption of Nenciu's super-adiabatic theory to C$^*$-dynamical systems and Bellissard's Ito derivatives w.r.t. the magnetic field., Comment: Errors and misprints corrected; introduction expanded; to appear in CMP

As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adiabatic limit the macroscopic current is determined by the geometry of the Bloch bundle. As a consequence we obtain the King-Smith and Vanderbilt formula up to errors smaller than any power of the adiabatic parameter., Comment: 34 pages, no figures

We describe here a novel way of defining Hamiltonians for quantum field theories (QFTs), based on the particle–position representation of the state vector and involving a condition on the state vector that we call an “interior–boundary condition.” At least for some QFTs (and, we hope, for many), this approach leads to a well-defined, self-adjoint Hamiltonian without the need for an ultraviolet cut-off or renormalization.

This article presents and evaluates a surface hopping algorithm for time-dependent two-level Schrödinger systems with conically intersecting eigenvalues. The algorithm implements an asymptotic semigroup for approximating the solution’s Wigner function, which was rigorously defined and derived from the Schrödinger equation by two of the authors in previous work. It is applied to two-dimensional isotropic systems, which include linear Jahn-Teller Hamiltonians and Gaussian initial data. It reproduces energy level populations and expectation values with an accuracy of two to three percent.

We consider a system of $N$ bosons confined to a thin waveguide, i.e.\ to a region of space within an $\varepsilon$-tube around a curve in $\mathbb{R}^3$. We show that when taking simultaneously the NLS limit $N\to \infty$ and the limit of strong confinement $\varepsilon\to 0$, the time-evolution of such a system starting in a state close to a Bose-Einstein condensate is approximately captured by a non-linear Schr\"odinger equation in one dimension. The strength of the non-linearity in this Gross-Pitaevskii type equation depends on the shape of the cross-section of the waveguide, while the "bending" and the "twisting" of the waveguide contribute potential terms. Our analysis is based on an approach to mean-field limits developed by Pickl., Comment: Final version to appear in Annales Henri Poincare

We consider the standard model problem for a conical intersection of electronic surfaces in molecular dynamics. Our main result is the construction of a semi-group in order to approximate the Wigner function associated with the solution of the Schrodinger equation at leading order in the semiclassical parameter. The semigroup stems from an underlying Markov process that combines deterministic transport along classical trajectories within the electronic surfaces and random jumps between the surfaces near the crossing. Our semigroup can be viewed as a rigorous mathematical counterpart of so-called trajectory surface hopping algorithms, which are of major importance in molecular simulations in chemical physics. The key point of our analysis, the incorporation of the nonadiabatic transitions, is based on the Landau-Zener type formula of Fermanian-Kammerer and Gerard10 for the propagation of two-scale Wigner measures through conical crossings. © 2005 Wiley Periodicals, Inc.

We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\phi(\epsi x)$, and vector potential $A(\epsi x)$, with $x \in \R^d$ and $\epsi \ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics., Comment: 37 pages

We propose a way of defining Hamiltonians for quantum field theories without any renormalization procedure. The resulting Hamiltonians, called IBC Hamiltonians, are mathematically well-defined (and in particular, ultraviolet finite) without an ultraviolet cut-off such as smearing out the particles over a nonzero radius; rather, the particles are assigned radius zero. These Hamiltonians agree with those obtained through renormalization whenever both are known to exist. We describe explicit examples of IBC Hamiltonians. Their definition, which is best expressed in the particle-position representation of the wave function, involves a kind of boundary condition on the wave function, which we call an interior-boundary condition (IBC). The relevant configuration space is one of a variable number of particles, and the relevant boundary consists of the configurations with two or more particles at the same location. The IBC relates the value (or derivative) of the wave function at a boundary point to the value of the wave function at an interior point (here, in a sector of configuration space corresponding to a lesser number of particles)., Comment: 27 pages LaTeX, 1 figure. The old version v1 has been (revised and) split into two papers, the first of which is v2 of this post, and the second of which is available as arXiv:1808.06262. v3, v4, v5: minor improvements, updated references, corrected prefactor in Eq. (58)

We consider an electron coupled to the quantized radiation field and subject to a slowly varying electrostatic potential. We establish that over sufficiently long times radiation effects are negligible and the dressed electron is governed by an effective one-particle Hamiltonian. In the proof only a few generic properties of the full Pauli–Fierz Hamiltonian H PF enter. Most importantly, H PF must have an isolated ground state band for |p| c ≤∞ with p the total momentum and p c indicating that the ground state band may terminate. This structure demands a local approximation theorem, in the sense that the one-particle approximation holds until the semiclassical dynamics violates |p| c . Within this framework we prove an abstract Hilbert space theorem which uses no additional information on the Hamiltonian away from the band of interest. Our result is applicable to other time-dependent semiclassical problems. We discuss semiclassical distributions for the effective one-particle dynamics and show how they can be translated to the full dynamics by our results.

The bone marrow provides niches for early B cell differentiation and long-lived plasma cells. Therefore, it has been hypothesized that perturbing bone homeostasis might impact B cell function and Ab production. This hypothesis is highly relevant for patients receiving long-term treatment with antiresorptive drugs. We therefore analyzed the humoral immune response of mice chronically treated with ibandronate, a commonly used bisphosphonate. We confirmed the increased bone mass caused by inhibition of osteoclast activity and also the strongly reduced bone formation because of decreased osteoblast numbers in response to ibandronate. Thus, bisphosphonate drastically inhibited bone remodeling. When ibandronate was injected into mice after a primary immunization to mimic common antiosteoporotic treatments, the generation of the various B cell populations, the response to booster immunization, and the generation of plasma cells were surprisingly normal. Mice also responded normally to immunization when ibandronate was applied to naive mice. However, there, ibandronate shunted the homing of bone marrow plasma cells. Interestingly, ibandronate reduced the numbers of megakaryocytes, a known component of the bone marrow plasma cell niche. In line with normal Ab responses, increased plasma cell populations associated with increased megakaryocyte numbers were then observed in the spleens of the ibandronate-treated mice. Thus, although inhibition of bone remodeling disturbed the bone marrow plasma cell niche, a compensatory niche may have been created by relocating the megakaryocytes into the spleen, thereby allowing normal B cell responses. Therefore, megakaryocytes may act as a key regulator of plasma cell niche plasticity.

We consider Schrodinger operators $$H=-\Delta _{g_\varepsilon } + V$$ on a fibre bundle $$M\mathop {\rightarrow }\limits ^{\pi }B$$ with compact fibres and a metric $$g_\varepsilon $$ that blows up directions perpendicular to the fibres by a factor $${\varepsilon ^{-1}\gg 1}$$ . We show that for an eigenvalue $$\lambda $$ of the fibre-wise part of H, satisfying a local gap condition, and every $$N\in \mathbb {N}$$ there exists a subspace of $$L^2(M)$$ that is invariant under H up to errors of order $$\varepsilon ^{N+1}$$ . The dynamical and spectral features of H on this subspace can be described by an effective operator on the fibre-wise $$\lambda $$ -eigenspace bundle $$\mathcal {E}\rightarrow B$$ , giving detailed asymptotics for H.

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schroedinger equation for the nuclei, including contributions from the Berry connection., Comment: Revised version. 19 pages, 2 figures

We consider the dynamics generated by the Schroedinger operator $H=-{1/2}\Delta + V(x) + W(\epsi x)$, where $V$ is a lattice periodic potential and $W$ an external potential which varies slowly on the scale set by the lattice spacing. We prove that in the limit $\epsi \to 0$ the time dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined by the semiclassical dynamics.

We simplify the proof of the adiabatic theorem of quantum mechanics without gap condition of Avron and Elgart by providing an elementary solution of the ‘commutator equation’. In addition, a minor modification of their argument allows for more direct treatment of eigenvalue crossings. We also obtain simple, explicit conditions that yield information on the rate of convergence in the adiabatic limit.

The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. The relation between these crossing probabilities and the usual formula for the scattering cross section is provided by the flux-across-surfaces theorem, which was conjectured by Combes, Newton, and Shtokhamer [Phys. Rev. D 11, 366–372 (1975)]. We prove the flux-across-surfaces theorem for short range potentials and wave functions without energy cutoffs. The proof is based on the free flux-across-surfaces theorem (Daumer et al.) [Lett. Math. Phys. 38, 103–116 (1996)], and on smoothness properties of generalized eigenfunctions: It is shown that if the potential V(x) decays like |x|−γ at infinity with γ>n∈N then the generalized eigenfunctions of the corresponding Hamiltonian −1/2Δ+V are n−2 times continuously differentiable with respect to the momentum variable.

Bone mass is maintained by osteoclasts that resorb bone and osteoblasts that promote matrix deposition and mineralization. Bone homeostasis is altered in chronic inflammation as well as in post-menopausal loss of estrogen, which favors osteoclast activity that leads to osteoporosis. The MAPK p38 alpha is a key regulator of bone loss and p38 inhibitors preserve bone mass by inhibiting osteoclastogenesis. p38 function is regulated by two upstream MAPK kinases, namely MKK3 and MKK6. The goal of this study was to assess the effect of MKK3- or MKK6-deficiency on osteoclastogenesis in vitro and on bone loss in ovariectomy-induced osteoporosis in mice. We demonstrated that MKK3 but not MKK6, regulates osteoclast differentiation from bone marrow cells in vitro. Expression of NFATc1, a master transcription factor in osteoclastogenesis, is decreased in cells lacking MKK3 but not MKK6. Expression of osteoclast-specific genes Cathepsin K, osteoclast-associated receptor and MMP9, was inhibited in MKK3-/- cells. The effect of MKK-deficiency on ovariectomy-induced bone loss was then evaluated in female WT, MKK3-/- and MKK6-/- mice by micro-CT analysis. Bone loss was partially inhibited in MKK3-/- as well as MKK6-/- mice, despite normal osteoclastogenesis in MKK6-/- cells. This correlated with the lower osteoclast numbers in the MKK-deficient ovariectomized mice. These studies suggest that MKK3 and MKK6 differentially regulate bone loss due to estrogen withdrawal. MKK3 directly mediates osteoclastogenesis while MKK6 likely contributes to pro-inflammatory cytokine production that promotes osteoclast formation.