Correlation functions of the one-dimensional Bose gas in the repulsive case

The one dimensional Bose gas is considered in the repulsive case. The ground state of the system is the Dirac sea with a finite density. The correlation function of the currents is presented in the form of the series, then ^th term being the contribution ofn vacuum particles. In the strong coupling limitc then ^th term decreases asc ^–n . In the weak coupling limitc 0 the series is also essentially simplified. The decomposition gives the uniform approximation in the distance between the currents. The arguments in favour of convergence of the series are given.     

Universality of entropy scaling in one dimensional gapless models

We consider critical models in one dimension. We study the ground state in the thermodynamic limit (infinite lattice). We are interested in an entropy of a subsystem. We calculate the entropy of a part of the ground state from a space interval (0,x). At zero temperature it describes the entanglement of the part of the ground state from this interval with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at any temperature. At zero temperature our formula reproduces a logarithmic formula, discovered by Vidal, Latorre, Rico, and Kitaev for spin chains. We prove our formula by means of conformal field theory and the second law of thermodynamics. Our formula is universal. We illustrate it for a Bose gas with a delta interaction and for the Hubbard model.     

Cyclic derivatives of 3-fluoro-3,3-dinitro-1-aminopropane

Conclusions A study was made of the preparation and nitrolysis of some cylic derivatives of 3-fluoro-3, 3-dinitro1-aminopropane, and the differences in the reactivity of the latter compound and the behavior of 3,3,3-trinitro-1-aminopropane in the same reactions were pointed out.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1369–1371, June, 1973.     

3-Fluoro-3,3-dinitro-1-aminopropane in the mannich reaction

Conclusions 3-Fluoro-3, 3-dinitro-1-aminopropane condenses with CH₂O and 1,1-dinitroalkanes to form Mannich bases which are readily converted to the corresponding N-nitro- and N-nitroso derivatives.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1876–1877, August, 1972.     

Pauli principle for one-dimensional bosons and the algebraic bethe ansatz

For the construction of the physical vacuum in exactly solvable one-dimensional models of interacting bosons it is important that the momenta of all the particles be different. We give a formal proof that they are indeed different.     

Synthesis of polynitroazaalkanols and some of their derivatives

Conclusions Polynitroazaalkanols and their chloro derivatives, nitrates, and acetates have been obtained for the first time.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 445–447, February, 1970.     

New N-nitrosoamines. 1. Synthesis and nitrosative cleavage of the Mannich bases derived from nitrogen-containing heterocycles and primary aliphatic amines

The reactions of isatin, benzotriazole, and succinimide with formaldehyde and methylamine yield monoamines RCH₂N(Me)CH₂R and methylenediamines RCH₂N(Me)CH₂N(Me)CH₂R. The use of ethylenediamine as the amino component affords N,N"-disubstituted imidazolidines, while the reactions with 3-aminopropan-1-ol give N-substituted tetrahydro-1,3-oxazines. RCH₂NBuⁱ ₂ was obtained from succinimide, formaldehyde, and diisobutylamine. Nitrosative cleavage of the amines obtained was studied; it was shown that monoamines and methylenediamines give N-nitrosoamines RCH₂N(NO)Me, which were structurally characterized by X-ray diffraction analysis. RCH₂NBuⁱ ₂ affords diisobutylnitrosamine, while imidazolidines transform into dinitroso compounds RCH₂N(NO)CH₂CH₂N(NO)CH₂R.