Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking

The lowest-energy state of a macroscopic system in which symmetry is spontaneously broken, is a very stable wavepacket centered around a spontaneously chosen, classical direction in symmetry space. However, for a Heisenberg ferromagnet the quantum groundstate is exactly the classical groundstate, there are no quantum fluctuations. This coincides with seven exceptional properties of the ferromagnet, including spontaneous time-reversal symmetry breaking, a reduced number of Nambu–Goldstone modes and the absence of a thin spectrum (Anderson tower of states). Recent discoveries of other non-relativistic systems with fewer Nambu–Goldstone modes suggest these specialties apply there as well. I establish precise criteria for the absence of quantum fluctuations and all the other features. In particular, it is not sufficient that the order parameter operator commutes with the Hamiltonian. It leads to a measurably larger coherence time of superpositions in small but macroscopic systems.     

Spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations

We study the spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations by separately calculating the contribution to the excitation rate of vacuum fluctuations and a cross term which involves both vacuum fluctuations and radiation reaction, and demonstrate that although the spontaneous excitation for the atom in its ground state would occur in vacuum, such atoms in circular motion do not perceive a pure thermal radiation as their counterparts in linear acceleration do since the transition rates of the atom do not contain the Planckian factor characterizing a thermal bath. We also find that the contribution of the cross term that plays the same role as that of radiation reaction in the scalar and electromagnetic fields cases differs for atoms in circular motion from those in linear acceleration. This suggests that the conclusion drawn for atoms coupled with the scalar and electromagnetic fields that the contribution of radiation reaction to the mean rate of change of atomic energy does not vary as the trajectory of the atom changes from linear acceleration to circular motion is not a general trait that applies to the Dirac field where the role of radiation reaction is played by the cross term.     

Wave-packet continuum discretization for quantum scattering

A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets which are the normalized states constructed from exact non-normalized continuum states. Projecting the wave functions and all scattering operators like t$t$-matrix, resolvent, etc. on such a wave-packet basis results in a formulation of quantum scattering problem entirely in terms of discrete elements and linear equations with regular matrices. It is demonstrated that there is a close relation between the above stationary wave packets and pseudostates which are employed often to approximate the scattering states with a finite L₂$L_2$ basis. Such a fully discrete treatment of complicated few- and many-body scattering problems leads to significant simplification of their practical solution. Also we get finite-dimensional approximations for complicated operators like effective interactions between composite particles constructed via the Feshbach-type projection formalism. As illustrations to this general approach we consider several important particular problems including multichannel scattering and scattering in the three-nucleon system within the Faddeev framework.     

Extreme beam attenuation in double-slit experiments: Quantum and subquantum scenarios

Combining high and low probability densities in intensity hybrids  , we study some of their properties in double-slit setups. In particular, we connect to earlier results on beam attenuation techniques in neutron interferometry and study the effects of very small transmission factors, or very low counting rates, respectively, at one of the two slits. We use a “superclassical” modeling procedure which we have previously shown to produce predictions identical with those of standard quantum theory. Although in accordance with the latter, we show that there are previously unexpected new effects in intensity hybrids for transmission factors below a?10⁻⁴$a?10^{-4}$, which can eventually be observed with the aid of weak measurement techniques. We denote these as quantum sweeper effects, which are characterized by the bunching together of low counting rate particles within very narrow spatial domains. We give an explanation of this phenomenology by the circumstance that in reaching down to ever weaker channel intensities, the nonlinear nature of the probability density currents becomes ever more important, a fact which is generally not considered–although implicitly present–in standard quantum mechanics.     

Design of Sensitive Biocompatible Quantum‐Dots Embedded in Mesoporous Silica Microspheres for the Quantitative Immunoassay of Human Immunodeficiency Virus‐1 Antibodies

A novel sandwich‐type electrochemiluminescence (ECL) immunosensor was developed to enable the sensitive detection of HIV‐1 antibodies. This system incorporated mesoporous silica (mSiO₂) complexed with quantum dots (QDs) and nano‐gold particles, which were assembled to enhance signal detection. Magnetic beads were used by immobilizing the secondary anti‐IgG antibody. This was first employed to capture HIV‐1 antibody (Ab) to form a Fe₃O₄/anti‐IgG/Ab complex. A high loading and signal‐enhanced nanocomposite (hereafter referred to as Au‐mSiO₂‐CdTe) was used as a HIV‐1 antigen label. The Au‐mSiO₂‐CdTe nanocomposite was conjugated with the Fe₃O₄/anti‐IgG/Ab complex to form an immunocomplex (hereafter referred to as Fe₃O₄/anti‐IgG/Ab/HIV‐1/CdTe‐mSiO₂‐Au). This complex could be further separated by an external magnetic field to produce ECL signals. Due to the large specific surface area and pore volume of mSiO₂, the loading of the CdTe QDs was markedly increased. Thus, the loaded QDs released a powerful chemiluminescent signal with a concordantly increased sensitivity of the immunosensor. The immunosensor was highly sensitive, and displayed a linear range of responses for HIV‐1 antibody across a dilution range of 1 : 1500 through 1 : 50 with the detection limit of 1 : 4500. The immunoassay can be a promising candidate in early diagnosis of HIV infection.     

Self-assembly and bioactivity of a polymer/peptide conjugate containing the RGD cell adhesion motif and PEG

The self-assembly and bioactivity of the peptide–polymer conjugate DGRFFF–PEG3000 containing the RGD cell adhesion motif has been examined, in aqueous solution. The conjugate is designed to be amphiphilic by incorporation of three hydrophobic phenylalanine residues as well as the RGD unit and a short poly(ethylene glycol) (PEG) chain of molar mass 3000 kg mol⁻¹. Above a critical aggregation concentration, determined by fluorescence measurements, signals of β-sheet structure are revealed by spectroscopic measurements, as well as X-ray diffraction. At high concentration, a self-assembled fibril nanostructure is revealed by electron microscopy. The fibrils are observed despite PEG crystallization which occurs on drying. This suggests that DGRFFF has an aggregation tendency that is sufficiently strong not to be prevented by PEG crystallization. The adhesion, viability and proliferation of human corneal fibroblasts was examined for films of the conjugate on tissue culture plates (TCPs) as well as low attachment plates. On TCP, DGRFFF–PEG3000 films prepared at sufficiently low concentration are viable, and cell proliferation is observed. However, on low attachment surfaces, neither cell adhesion nor proliferation was observed, indicating that the RGD motif was not available to enhance cell adhesion. This was ascribed to the core–shell architecture of the self-assembled fibrils with a peptide core surrounded by a PEG shell which hinders access to the RGD unit.     

Channel capacities via p-summing norms

In this paper we show how the metric theory of tensor products developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in Shannon's information theory. Furthermore, in the last years Shannon's theory has been fully generalized to the quantum setting, and revealed qualitatively new phenomena in comparison. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. These capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. Our approach to restricted capacities is based on tools from functional analysis, and in particular the notion of p  -summing maps going back to Grothendieck's work. Pisier's noncommutative vector-valued _Lp$L_p$ spaces allow us to establish the new connection between functional analysis and information theory in the quantum setting.     

Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra

Let U(g)$U(\mathfrak{g})$ be the enveloping algebra of a finite dimensional reductive Lie algebra g$\mathfrak{g}$ over an algebraically closed field of prime characteristic. Let _U?,P(s:)$U_{?,P}(\mathfrak{s}:)$ be the simply connected quantum enveloping algebra at the root of unity ?  , of a complex semi-simple finite dimensional Lie algebra s:$\mathfrak{s}:$. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange [32] (by different methods), the second one confirms a conjecture in [4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic.