The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure

Regularization of multi-soliton form factors in sine-Gordon model

A general and systematic regularization is developed for the exact solitonic form factors of exponential operators in the (1+1)-dimensional sine-Gordon model by analytical continuation of their integral representations. The procedure is implemented in Mathematica. Test results are shown for four- and six- soliton form factors.Comment: 12 pages, no figures. v2: minor corrections, some references adde

Nucleation control of quantum dot synthesis in a microfluidic continuous flow reactor

The use of microfluidics in chemical synthesis is topical due to the potential to improve reproducibility and the ability promptly interrogate a wide range of reaction parameters, the latter of which is necessary for the training of artificial intelligence (AI) algorithms. Applying microfluidic techniques to semiconductor nanocrystals, or quantum dots (QDs), is challenging due to the need for a high-temperature nucleation event followed by particle growth at lower temperatures. Such a high-temperature gradient can be realized using complex, segmented microfluidic reactor designs, which represents an engineering approach. Here, an alternative chemical approach is demonstrated using the cluster seed method of nanoparticle synthesis in a simple microfluidic reactor system. This enables quantum dot nucleation at lower temperatures due to the presence of molecular organometallic compounds (NMe4)4[Cd10Se4(SPh)16] and (NMe4)4[Zn10Se4(SPh)16]. This integration of cluster seeding with microfluidics affords a new mechanism to tailor the reaction conditions for optimizing yields and tuning product properties

Relative entanglement entropies in 1 + 1-dimensional conformal field theories

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(\u3c11\u2016\u3c10) between two given reduced density matrices \u3c11 and \u3c10 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(\u3c11\u3c1n 1210) and define a set of R\'enyi relative entropies Sn(\u3c11\u2016\u3c10). We compute these quantities for integer values of the parameter n and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i 02\u3d5, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. \ua9 2017, The Author(s)

Quantum Entanglement of Localized Excited States at Finite Temperature

In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.Comment: 1+28 pages, 12 figures, v2 reference adde