Small Coupling Constant Research Articles

Fluctuations of the solutions to the KPZ equation in dimensions three and higher

We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in $$d\ge 3$$ with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger (J Stat Phys 171:543–598, 2018).

Gaussian fluctuations from the 2D KPZ equation

We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards-Wilkinson equation with an effective variance.

Non-Markovian dynamics of a dephasing model in a squeezed thermal bath

The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.

Pushing resolution limits for extracting 1H-1H scalar coupling constants by a resolution-enhanced selective refocusing method.

Nuclear magnetic resonance (NMR) spectroscopy enables one to study molecular structure and dynamics in a noninvasive manner and has long served as a versatile and indispensable analytical tool in physics, chemistry, and biology. Scalar coupling, an essential feature in NMR spectroscopy, provides rich information regarding molecular structure and conformation. The measurement of scalar coupling constants, therefore, constitutes an important issue in NMR spectroscopy. Homonuclear 2D J-resolved spectroscopy is a powerful tool for multiplet analysis and coupling measurement. Recently, a number of phase-sensitive J-resolved methods and selective measuring methods have been developed to facilitate the extraction of coupling constants. However, resolution remains a crucial challenge when extracting small coupling constants or under inhomogeneous fields. In this paper, we present a resolution-enhanced selective refocusing (RESERF) method for the extraction of coupling constants. The effect of magnetic field inhomogeneity can be eliminated, resulting in very narrow linewidths. Therefore, samples with small coupling constants or under inhomogeneous fields can be well analyzed. The RESERF method may be of great value for structural and conformational studies in chemistry and biology.

Variational Approximations for Intersite Soliton in a Ablowitz-Ladik-Cubic Discrete Nonlinear Schrödinger Equation

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Existence and nonexistence of bound state solutions for Schrödinger systems with linear and nonlinear couplings

We study the Schrödinger systems with linear and nonlinear coupling terms (doubly coupled nonlinear Schrödinger system for short) which arise naturally in nonlinear optics, and in the Hartree–Fock theory for Bose–Einstein condensates, among other physical problems. First, for small linear coupling constant, we get existence of a nontrivial bound state solution to the system via perturbation method, furthermore, we prove each component of the bound state solution is nonnegative by energy estimate. Second, we establish a version of Pohozaev–Nehari identity and prove a nonexistence result for the more general system when the spatial dimension N ≥ 4 .

High Resolution for Chemical Shifts and Scalar Coupling Constants: The 2D Real‐Time J‐Upscaled PSYCHE‐DIAG

The facile determination of chemical shift and scalar coupling constants in NMR spectra is often prevented by spectral overlap and limited resolution. Here, we present a high-resolution NMR experiment for the simultaneous detection of both resonance frequencies and coupling patterns even with small J-values. A PSYCHE-decoupled DIAG (Pure Shift Yielded by Chirp Excitation- DIAGonal) experiment, which resolves chemical shift in the indirect dimension of a 2D experiment is combined with real-time J-upscaling in order to visualize small coupling constants that would otherwise be hidden in the linewidth of a regular proton or DIAG spectrum.

A Monodromy Matrix for the Almost Mathieu Equation with Small Coupling Constant

For the almost Mathieu operator with small coupling constant, we describe the asymptotics of a monodromy matrix and of a series of spectral gaps.

Analysis of time-resolved EPR spectra observed in the photolysis of disulphonated anthraquinones included in cyclodextrins – evidence of the S-T_ mixing of radical pair mechanism

ABSTRACTCyclodextrins (CDs) are well known hosts of inclusion compounds, and they can be used for molecular identification and separation. Several studies have already been reported from the point of view of photchemistry and spin-chemistry. These reports showed that the inside environment of CDs such as their bore-size works for their specific properties. In this report, the time-resolved EPR spectra observed in the photolysis of aqueous solution of disulphonated anthraquinones included in β-CD and γ-CD are carefully analysed. The spectral simulation employing Radical Pair Mechanism (RPM) of Chemically Induced Dynamic Electron Polarisation is carried out. Finally, it is concluded that the peculiar hyperfine-dependence observed in these particular systems is exclusively caused by the mixing RPM, despite the radical pairs (RPs) having small hyperfine coupling (HFC) constants (less than 3.4 mT). Another finding is the quenching of the spin polarisation of the RP conveyed from the excited triplet state of anthraquinones before mixing. This is explained as arising from slow relative diffusional motion of the RP members when included in the interior of the CDs. General expression of the and S-T+ mixing of multiple nuclei (I = 1/2) with different conditions such as the spin multiplicity of the precursor molecule and the sign of the HFC constants, is also suggested.

Nuclear Matter Under Extreme Conditions: from Quark-Gluon Plasma to Neutron Stars

Most of the mass in the Universe is dynamically generated by the strong interaction that can be described by the Quantum Chromodynamics (QCD) in the present Standard Model. However, QCD works only in the limit of asymptotic freedom with small coupling constant at high energies. When the two heavy ions collide each other at high energies, very dense quark-gluon matter (the so-called quark-gluon plasma or QGP) is formed, and QCD cannot properly describe the dynamics in QGP at present. Another major trend in the contemporary QCD research is to explore the neutron-rich nuclear matter produced by the radioactive ion beams. Such an abnormal state of the strongly interacting matter is conjectured to be the core of the neutron star. The dense neutron-rich matter is expected to be the ground of the various exotic phenomena like kaon condensation. Understanding the structure and the dynamics of the neutron matter is one of the major research topics in not only nuclear physics but also astrophysics. In this review, the status and future perspectives of the research on nuclear matter under extreme conditions are briefly summarized.

Discretisations of rough stochastic PDEs

We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that the dynamical $\Phi^{4}_{3}$ model on the dyadic grid converges after renormalisation to its continuous counterpart. This result in particular implies that, as expected, the $\Phi^{4}_{3}$ measure with a sufficiently small coupling constant is invariant for this equation and that the lifetime of its solutions is almost surely infinite for almost every initial condition.

Redox-Active Metallodithiolene Groups Separated by Insulating Tetraphosphinobenzene Spacers.

Compounds of the type [(S2C2R2)M(μ-tpbz)M(S2C2R2)] (R = CN, Me, Ph, p-anisyl; M = Ni, Pd, Pt; tpbz = 1,2,4,5-tetrakis(diphenylphosphino)benzene) have been prepared by transmetalation with [(S2C2R2)SnR'2] reagents, by direct displacement of dithiolene ligand from [M(S2C2R2)2] with 0.5 equiv of tpbz, or by salt metathesis using Na2[S2C2(CN)2] in conjunction with X2M(μ-tpbz)MX2 (X = halide). X-ray crystallography reveals a range of topologies (undulating, chair, bowed) for the (S2C2)M(P2C6P2)M(S2C2) core. The [(S2C2R2)M(μ-tpbz)M(S2C2R2)] (R = Me, Ph, p-anisyl) compounds support reversible or quasireversible oxidations corresponding to concurrent oxidation of the dithiolene terminal ligands from ene-1,2-dithiolates to radical monoanions, forming [(-S•SC2R2)M(μ-tpbz)M(-S•SC2R2)]2+. The R = Ph and p-anisyl compounds support a second, reversible oxidation of the dithiolene ligands to their α-dithione form. In contrast, [(S2C2(CN)2)Ni(tpbz)Ni(S2C2(CN)2)] sustains only reversible, metal-centered reductions. Spectroscopic examination of [(-S•SC2( p-anisyl)2)Ni(μ-tpbz)Ni(-S•SC2( p-anisyl)2)]2+ by EPR reveals a near degenerate singlet-triplet ground state, with spectral simulation revealing a remarkably small dipolar coupling constant of 18 × 10-4 cm-1 that is representative of an interspin distance of 11.3 Å. This weak interaction is mediated by the rigid tpbz ligand, whose capacity to electronically insulate is an essential quality in the development of molecular-based spintronic devices.

Extracting unresolved coupling constants from complex multiplets by a real‐time J‐upscaled SERF experiment

The measurement of small homonuclear coupling constants is often prevented by either their small size and/or overlap with other signal splittings. Here, we present a real‐time method to extract such couplings without interference from other splittings, with a resolution that is beyond conventional NMR spectra. In this real‐time J‐upscaled SERF experiment, homonuclear coupling is removed by slice‐selective pure shift NMR, whereas scalar coupling to only one selected signal is reintroduced by selective refocusing. The remaining couplings are enhanced by real‐time J‐upscaling during interruptions of the FID data acquisition. The resulting spectrum is not only simplified by the restriction of the scalar coupling but also its resolution enhanced. This improved resolution results from a reduction of signal broadening due to magnetic field inhomogeneities from 2 different sources: slice‐selective excitation and the spin‐echo type J‐upscaling element.

Discrepancy Between Experimental and Theoretical Predictions of the Adiabaticity of Ti+ +CH3 OH.

The reaction between Ti+ and methanol (CH3 OH) is a model system for competition between activation of C-O, C-H, and O-H bonds and of the role of excited electronic pathways in catalytic processes. Herein, we use experimental kinetics, quantum chemical calculations, and statistical modeling to identify the critical features of the reaction's potential energy surface. Experimental kinetics data between 300 and 600 K shows the reaction largely proceeds through C-O bond activation, yielding TiOH+ and TiO+ . Products of the O-H activation pathway, TiOCH2+ and TiOCH3+ are minor, whereas C-H bond activation is not observed at thermal energies. Statistical modeling well-reproduces the experimental results and offers insight into the reaction mechanism. Notably, efficient spin-crossing along the C-O activation pathway is required to produce the observed product distribution, in contrast to a previous estimate of inefficient crossing based on calculation of a small spin-orbit coupling constant. This discrepancy highlights a potential limitation of simple models within the Landau-Zener framework, which are commonly used to calculate surface-crossing probabilities in reactive systems.

Suppression of decoherence of a spin–boson system by time-periodic control

We consider a finite-dimensional quantum system coupled to the bosonic radiation field and subject to a time-periodic control operator. Assuming the validity of a certain dynamic decoupling condition, we approximate the system’s time evolution with respect to the non-interacting dynamics. For sufficiently small coupling constants g and control periods T, we show that a certain deviation of coupled and uncoupled propagator may be estimated by $$\mathcal {O}(gt \, T)$$ . Our approach relies on the concept of Kato stability and general theory on non-autonomous linear evolution equations.

Elimination of signals tilting caused by B0 field inhomogeneity using 2D-lineshape reference deconvolution

An efficient approach for reference deconvolution of two-dimensional spectra aiming at the correction of static field inhomogeneity was established. In comparison to known techniques, a great improvement was achieved using the cross-section along the diagonal of the reference peak instead of its full 2D line shape. The method is termed pseudo-2D diagonal deconvolution. The approach developed allows suppressing the two-dimensional peaks tilting caused by the magnetic field inhomogeneity, while keeping the signal-to-noise ratio constant. Long-known method of 2D reference deconvolution (true-2D reference deconvolution) was also applied for comparison. The neutral and resolution-enhancing pseudo-2D deconvolutions were successfully applied for the resolution of complex overlapping multiplets and for measuring small scalar coupling constants. The new algorithm for the elimination of shape distortion of two-dimensional peaks showed to be promising in the perspective of an automated analysis of 2D correlation NMR spectra.

Efficient emitting molecules in organic light-emitting diodes on the basis of the control of vibronic couplings

A high external quantum efficiency observed in organic light-emitting diodes using PTZ-BZP (PTZ: 10-hexyl-phenothiazin, and BZP: 4-phenyl-2,1,3-benzothiadiazole) as an emitting molecule is studied based on the vibronic coupling density analyses employing the time-dependent density functional theory. The high efficiency can be attributed to a high efficiency of exciton generation which originates from reverse intersystem crossings from the higher T3 and T2 states than T1 to the emitting S1 state. The nonradiative transitions from T3 and T2 to the lower triplet states are suppressed because of small offdiagonal vibronic coupling constants. The small vibronic couplings originate from the multi-configurationality of these triplet states. A molecular design principle for efficient emitting molecules is discussed from the view of the control of vibronic couplings.

Evidence for interacting dark energy from BOSS

The result presented by the BOSS-SDSS Collaboration measuring the baryon acoustic oscillations of the Lyman-$\alpha$ forest from high-redshift quasars indicates a $2.5\sigma$ departure from the standard $\Lambda$-cold-dark-matter model. This is the first time that the evolution of dark energy at high redshifts has been measured, and the current results cannot be explained by simple generalizations of the cosmological constant. We show here that a simple phenomenological interaction in the dark sector provides a good explanation for this deviation, naturally accommodating the Hubble parameter obtained by BOSS, $H(z=2.34)=222 \pm 7 ~\mathrm{km~s^{-1}~Mpc^{-1}}$. By performing a global fit of the parameters with the inclusion of this new data set together with the Planck data for the interacting model, we are able to show that some interacting models have constraints for $H(2.34)$ and $D_\mathrm{A}(2.34)$ that are compatible with the ones obtained by the BOSS Collaboration, showing a better concordance than $\Lambda$CDM. We also show that the interacting models that have a small positive coupling constant, which helps alleviate the coincidence problem, are compatible with the cosmological observations. Adding the likelihood of these new baryon acoustic oscillations data shows an improvement in the global fit, although it is not statistically significant. The coupling constant could not be fully constrained by the data sets used, but the dark energy equation of state shows a slight preference for a value different from a cosmological constant.

On condensate of solutions for the Chern–Simons–Higgs equation

This is the first part of our comprehensive study on the structure of doubly periodic solutions for the Chern–Simons–Higgs equation with a small coupling constant. We first classify the bubbling type of the blow-up point according to the limit equations. Assuming that all the blow-up points are away from the vortex points, we prove the non-coexistence of different bubbling types in a sequence of bubbling solutions. Secondly, for the CS type bubbling solutions, we obtain an existence result without the condition on the blow-up set as in [4]. This seems to be the first general existence result of the multi-bubbling CS type solutions which is obtained under nearly necessary conditions. Necessary and sufficient conditions are also discussed for the existence of bubbling solutions blowing up at vortex points.

Singlet versus Triplet Reactivity in an Mn(V)-Oxo Species: Testing Theoretical Predictions Against Experimental Evidence.

Discerning the factors that control the reactivity of high-valent metal-oxo species is critical to both an understanding of metalloenzyme reactivity and related transition metal catalysts. Computational studies have suggested that an excited higher spin state in a number of metal-oxo species can provide a lower energy barrier for oxidation reactions, leading to the conclusion that this unobserved higher spin state complex should be considered as the active oxidant. However, testing these computational predictions by experiment is difficult and has rarely been accomplished. Herein, we describe a detailed computational study on the role of spin state in the reactivity of a high-valent manganese(V)-oxo complex with para-Z-substituted thioanisoles and utilize experimental evidence to distinguish between the theoretical results. The calculations show an unusual change in mechanism occurs for the dominant singlet spin state that correlates with the electron-donating property of the para-Z substituent, while this change is not observed on the triplet spin state. Minimum energy crossing point calculations predict small spin-orbit coupling constants making the spin state change from low spin to high spin unlikely. The trends in reactivity for the para-Z-substituted thioanisole derivatives provide an experimental measure for the spin state reactivity in manganese-oxo corrolazine complexes. Hence, the calculations show that the V-shaped Hammett plot is reproduced by the singlet surface but not by the triplet state trend. The substituent effect is explained with valence bond models, which confirm a change from an electrophilic to a nucleophilic mechanism through a change of substituent.