Sub-poissonian statistics of fluorescence photons of a single molecule

The method previously used by the author for the measurement and calculation of the distribution function w _N(T)of fluorescence photons from a single two-level atom that is continuously excited by laser light and has a unity fluorescence quantum yield is generalized to the case of a single molecule whose fluorescence quantum yield is smaller than unity and to the case of a three-level molecule whose fluorescence is blinking. The functions w _N(T) calculated for these two cases demonstrate a sub-Poissonian distribution of fluorescence photons.     

Photon distribution function in blinking fluorescence of individual molecules

A photon distribution function w_N(T) for blinking fluorescence with bright on- and dark off-intervals is derived. The function w_N(T) is expressed via few Poissonian functions each of which relates to corresponding exponential process in quantum dynamics of a given individual molecule. The distribution of photons is calculated for short, middle and long time intervals as compared to off-intervals. The distributions are much broader than Poissonian distribution and have rather complicated shape. If time resolution of an experiment does not permit us to see off-interval and, therefore, fluorescence looks like CW emission, the distribution of photons gives a signal about existence of hidden off- intervals in such CW fluorescence.     

Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work.     

Theory of the spectral acoustic phonon emission intensity of hot 2D electrons in quantized n-inversion layers

The spectral acoustic phonon emission intensity of the hot quasi two-dimensional electron gas (2DEG) in quantized n-Si (GaAs) inversion layers is calculated as a function of the phonon angular frequency w at different values of the carrier temperature T_e and density N_s. In the long wave length limit (ℏw ⪡ k_BT_e) the emission intensity increases ∝ w^s(w^s+1) for bulk- (surface-) modes where s = 3 for the unscreened acoustic deformation potential coupling. At w ≈ v_j2k_F (v_j: sound velocity of the phonon mode j, k_F: radius of the Fermi-circle) the emission intensity reaches a maximum whose position is shifted to higher w-values if N_s increases. For given values of N_s, T_e, T (lattice temperature) and ϑ (emission angle) the emission intensity maximum of the n-GaAs inversion layer is found to be about one order of magnitude smaller than the intensity maximum of the n-Si inversion layer.     

Dynamical theory for photon and photoelectric pulse distributions in single molecule fluorescence

A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function w_N(t) and for the photoelectric pulse distribution function f_n(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. f_n(t) ≅ w_N(t). A relation between w_N(t) and f_n(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k.     

4D localization in Randall-Sundrum 2 supergravity and in Vasiliev theories

We discuss the problem of localization of 4D massless states in Randall-Sundrum 2 (one-brane) models. A Randall-Sundrum 2 construction starting from N=8 gauged supergravity in 5D anti-de Sitter space gives rise to an N=4 supergravity-matter system. We explicitly show that only the modes of the N=4 graviton supermultiplet localize on the 4D brane, streamlining and generalizing previous works. We also point out that while charged 1/4 BPS black holes do exist in the 4D theory, they are always produced in sets of total charge zero. This zero-charge configuration uplifts to a 5D metric without naked singularities, thus avoiding the curvature singularity of the 5D uplift of an isolated charged BPS black hole. Finally, we resolve a puzzle with localization of massless high spin fields on a (putative) Randall-Sundrum 2 construction based on Vasiliev?s high spin theories. We show that while high spin fields do localize, the gauge symmetry that ensures decoupling of their unphysical polarizations is anomalous. This implies that the high spin fields must acquire a mass.     

Extremes of N Vicious Walkers for Large N: Application to the Directed Polymer and KPZ Interfaces

We compute the joint probability density function (jpdf) P _N (M,?? _M ) of the maximum M and its position ?? _M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N????, this jpdf is peaked around $M = \sqrt{2N}$ and ?? _M =1/2, while the typical fluctuations behave for large N like $M - \sqrt{2N} \propto s N^{-1/6}$ and ?? _M ?1/2??wN ^?1/3 where s and w are correlated random variables. One obtains an explicit expression of the limiting jpdf P(s,w) in terms of the Tracy-Widom distribution for the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory and a psi-function for the Hastings-McLeod solution to the Painlevé II equation. Our result yields, up to a rescaling of the random variables s and w, an expression for the jpdf of the maximum and its position for the Airy₂ process minus a parabola. This latter describes the fluctuations in many different physical systems belonging to the Kardar-Parisi-Zhang (KPZ) universality class in 1+1 dimensions. In particular, the marginal probability density function (pdf) P(w) yields, up to a model dependent length scale, the distribution of the endpoint of the directed polymer in a random medium with one free end, at zero temperature. In the large w limit one shows the asymptotic behavior logP(w)???w ³/12.     

Bistability of radiation force on N-atom system

We consider a system with N two-level atoms in a cavity, interacting with an external radiation field. Using Ehrenfest's theorem the radiation force on the N-atom system is studied as a function of the external radiation field. In a certain parameter region we are able to show that the radiation force can be bistable     

Surface Thermodynamics,Viscosity, Activation Energy of N-Methyldiethanolamine Aqueous Solutions Promoted by Tetramethylammonium Arginate

The surface tension and viscosity values of N-methyldiethanolamine (MDEA) aqueous solutions promoted by tetramethylammonium arginate ([N₁₁₁₁][Arg]) were measured and modeled. The experimental temperatures were 303.2 to 323.2 K. The mass fractions of MDEA (w_MDEA) and [N₁₁₁₁][Arg] (w_[N1111][Arg]) were 0.300 to 0.500 and 0.025 to 0.075, respectively. The measured surface tension and viscosity values were satisfactorily fitted to thermodynamic models. With the aid of experimentally viscosity data, the activation energy (Ea) and H₂S diffusion coefficient (D_H2S) of MDEA-[N₁₁₁₁][Arg] aqueous solution were deduced. The surface entropy and surface enthalpy of the solutions were calculated using the fitted model of the surface tension. The quantitative relationship between the calculated values (surface tension, surface entropy, surface enthalpy, viscosity, activation energy, and H₂S diffusion coefficient) and the operation conditions (mass fraction and temperature) was demonstrated.     

Model study on disordered one-dimensional microstructures

Using a finite Kronig-Penney model the localization behavior is studied as a function of disorder and sample size for individual realizations as well as for ensembles. There is a number of effects typical for small disordered systems: e.g. level repulsion is found to be connected with resonant delocalization, and there is a pronounced N-odd/N-even effect in the transmission coefficient. Opposite to the thermodynamic limit the ensemble shows weakest fluctuation in the average transmission coefficient rather than in the average localization length. The 3-dimensional extension of the model which still behaves one-dimensional, demonstrates the importance of spatial correlations in addition to disorder strength.     

Theory of the hot free carrier intraband-absorption coefficient of n-inversion layers

The absorption coefficient K of a quasi two dimensional (2D) hot free electron gas is calculated for the first time as a function of the lattice temperature T, the photon angular frequency w, the carrier density N_s as well as the electron temperature T_e when the carriers are scattered by ionized impurities, acoustic phonons and polar optical phonons. Analytical expressions are derived in the limiting cases of non-degeneracy and degeneracy of the electron system. In the quantum limit ħw/k_BT_e ≳ 1 where the interaction between the electron and the photon is inelastic K sensitively depends on the limiting scattering mechanism showing that the electron motion is completely controlled by the photon field. In the classical limit ħw/k_BT_e ⪡ 1 the absorption decreases proportional to w¹ independent of the limiting scattering mechanism in agreement with the experimental data deduced from far-infrared absorptivity measurements on GaAs heterolayers.     

Universal relation between Green functions in random matrix theory

We prove that in random matrix theory there exists a universal relation between the onepoint Green function G and the connected two-point Green function G_c given by N²G_c(z, w) = (∂²/∂z ∂w) log[(G(z) − G(w))/(z − w) + irrelevant factorized terms]. This relation is universal in the sense that it does not depend on the probability distribution of the random matrices for a broad class of distributions, even though G is known to depend on the probability distribution in detail. The universality discussed here represents a different statement than the universality we discovered some time ago, which states that a²G_c (az, aw) is independent of the probability distribution, where a denotes the width of the spectrum and depends sensitively on the probability distribution. It is shown that the universality proved here also holds for the more general problem of a hamiltonian consisting of the sum of a deterministic term and a random term analyzed perturbatively by Brézin, Hikami, and Zee.     

A new code construction with zero cross correlation based on BIBD

This paper presents a newly constructed zero cross correlation code (ZCC) which is based on BIBD (balanced incomplete block design) code. The ZCC (C, w) code is a family of binary sequences of length C and constant Hamming-weight w. Such codes find applications in spectral amplitude-coding optical code division multiple access (SAC-OCDMA). The constructing ZCC codes have a size of C ? N ÿ w + 1, where N is the number of users and C is any prime number. The proposed construction method is not complicated compared to the existing ones.     

Exactly solvable model of a spin glass

Sherrington and Kirkpatrick presented a solvable model of a spin glass. In the solution, they used a mathematically unwarranted procedure. In the present article, we show that the problem is exactly solved by starting with the virial expansion formula, and confirm the results of Sherrington and Kirkpatrick. The solution is obtained for the random Ising magnet in which the external field of each site and the exchange integral between each pair of sites are random variables. We obtain the exact thermodynamic properties for this system in the limit of n_w→∞, assuming that the exchange integrals of a spin with O(n_w) neighbours are $\text{O(n}{}_{\mathrm{w}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ and the average value of each is O(n_w^?1). The system is found to show the spin-glass state as well as the paramagnetic and the ferromagnetic state.     

Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators

We study the bifurcation and dynamical behaviour of the system of N globally coupled identical phase oscillators introduced by Hansel, Mato and Meunier, in the cases N=3 and N=4. This model has been found to exhibit robust ‘slow switching’ oscillations that are caused by the presence of robust heteroclinic attractors. This paper presents a bifurcation analysis of the system in an attempt to better understand the creation of such attractors. We consider bifurcations that occur in a system of identical oscillators on varying the parameters in the coupling function. These bifurcations preserve the permutation symmetry of the system. We then investigate the implications of these bifurcations for the sensitivity to detuning (i.e. the size of the smallest perturbations that give rise to loss of frequency locking).For N=3 we find three types of heteroclinic bifurcation that are codimension-one with symmetry. On varying two parameters in the coupling function we find three curves giving (a) an S₃-transcritical homoclinic bifurcation, (b) a saddle-node/heteroclinic bifurcation and (c) a Z₃-heteroclinic bifurcation. We also identify several global bifurcations with symmetry that organize the bifurcation diagram; these are codimension-two with symmetry.For N=4 oscillators we determine many (but not all) codimension-one bifurcations with symmetry, including those that lead to a robust heteroclinic cycle. A robust heteroclinic cycle is stable in an open region of parameter space and unstable in another open region. Furthermore, we verify that there is a subregion where the heteroclinic cycle is the only attractor of the system, while for other parts of the phase plane it can coexist with stable limit cycles. We finish with a discussion of bifurcations that appear for this coupling function and general N, as well as for more general coupling functions.     

Paramagnetic–ferrimagnetic transition in strong coupling paramagnetic systems: effect of cubic anisotropy interaction

The purpose of the present work is a quantitative investigation of the biquadratic exchange interaction effects on the paramagnetic–ferrimagnetic transition arising from two strongly coupled paramagnetic (1-spin) sublattices, of respective moments m and M. The free energy describing the physics of the system is of Landau type. In addition to the quadratic and quartic terms, in both m and M, this free energy involves two mixing interaction terms. The first is a lowest order coupling −CmM, where C<0 stands for the coupling constant measuring the interaction between the two sublattices. While the second, which is relevant for 1-spin systems and which traduces the dipole–dipole (or biquadratic) interaction, is of type wm²M², where w>0 is the new coupling constant. These two interactions enter in competition, and then, they induce drastic changes of the magnetic behavior of the material. The main change is that, the presence of this high order coupling tends to destroy the ferrimagnetic order of the system. We first show that the introduction of this biquadratic interaction does not affect the values of critical exponents. Also, we find that the compensation temperature (when it exists) and the compensation magnetic field are shifted to their lowest values, in comparison with the w=0 case. The Arrott-phase-diagram shape is also investigated quantitatively. We show the existence of three regimes depending on the values of w. When the latter is small, we find that the region of competition between the coupling C and the applied magnetic field H becomes more narrow under the effect of w (by competition, we mean the passage from the antiparallel state to the parallel one). While for higher values of w, this competition disappears completely, and then, the system loses its ferrimagnetic character. Kinetics of the phase transition is also examined, when the temperature is lowered from an initial value T_i to a final one T_f very close to the critical temperature T_c. As in the w=0 case, we find that kinetics is controlled by two kinds of relaxation times τ₁ and τ₂. The former is the relevant time, and is associated to long-wavelength fluctuations driving the system to undergo a phase transition. The second is a short time, which controls local dynamics. Near T_c, we show that, in particular, the longest relaxation time τ₁ becomes less important in comparison with that relative to the w=0 case. Finally, we note that the existence of two relaxation times is consistent with the predictions of a recent experiment, which was concerned with the 1/2-spin compounds Li_xNi_2−xO₂, where the composition x is close to 1.     

Photon distribution functions of the fluorescence photons from a single nanoparticle in various photon counting methods

Simple expressions have been derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. In contrast to the previously derived expressions represented in the form of N multiple integrals, the new expressions contain only single or double integrals of Poisson functions, which makes it possible to easily perform the numerical calculation of the photon distribution. The simplest photon counting method corresponds to the lengthiest function w _N ^M (T); on the contrary, the simplest function w _N ^O (T) corresponds to the most complex photon counting method. The functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) are noticeably different in short time intervals T; however, the distributions calculated using these functions are almost indistinguishable from each other in long T intervals. This circumstance makes it possible to use the simplest function w _N ^O (T) to consider the photon statistics measured by the simplest method. This possibility is particularly important for investigating the fluorescence photon statistics, where the intensity fluctuates.     

Nanosecond and femtosecond UV laser ablation of polymers: Influence of molecular weight

We examine the nanosecond and femtosecond UV laser ablation of poly(methyl methacrylate) (PMMA) as a function of molecular weight (M_w). For laser ablation with nanosecond laser pulses, at the excimer wavelengths 248 nm and 193 nm, we show that high temperatures develop; yet the dynamics of material ejection differs depending on polymer M_w. The results on the nanosecond ablation of polymers are accounted within the framework of bulk photothermal model and the results of molecular dynamics simulations. Turning next to the 248 nm ablation with 500 fs laser pulses, the ablation threshold and etching rates are also found to be dependent on polymer M_w. In addition, ablation results in morphological changes of the remaining substrate. Plausible mechanisms are advanced.     

More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s)

In this paper we provide strong evidence that there is no ambiguity in the choice of the horizon function underlying the Gribov–Zwanziger action. We show that there is only one correct possibility which is determined by the requirement of multiplicative renormalizability. As a consequence, this means that relations derived from other horizon functions cannot be given a consistent interpretation in terms of a local and renormalizable quantum field theory. In addition, we also discuss that the Kugo–Ojima functions u(p ²) and w(p ²) can only be defined after renormalization of the underlying Green function(s).