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Šamaj, L.; Travěnec, Igor

doi:10.1023/a:1026489924895

Cited by 56 publications

(69 citation statements)

References 17 publications

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“…It is also interesting to note that our expressions for the two-point fermion correlators of the MTM, (19) and (20) reproduce, in the case β 2 = 4π (free-fermion point) the free massive fermion correlation function…”

Section: Bipolar Coordinates and The Fermion Correlatorsmentioning

confidence: 64%

“…Notice that the coefficients C +(−) n and F +(−) n in (19) and (20) depend on | x − y| through the restriction on the integration region given by (18).…”

Section: Bipolar Coordinates and The Fermion Correlatorsmentioning

confidence: 99%

“…Indeed, for β 2 = 4π the series appearing in (19) and (20), respectively, are precisely the ones that occur in the definition of the Bessel functions K 1 and K 0 [29]. Equating the coefficients we obtain the following expressions for C …”

Section: Bipolar Coordinates and The Fermion Correlatorsmentioning

confidence: 99%

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Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Mondaini¹,

Marino²

2006

J. Phys. A: Math. Gen.

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Abstract. We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for β 2 = 8π, they reproduce the exactly known corresponding functions of the massless theory, explicitly confirming the irrelevance of the mass term at this point. This result is obtained by using the Coulomb gas representation of the fermionic MTM correlators in the bipolar coordinate system.

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Section: Bipolar Coordinates and The Fermion Correlatorsmentioning

confidence: 64%

“…Notice that the coefficients C +(−) n and F +(−) n in (19) and (20) depend on | x − y| through the restriction on the integration region given by (18).…”

Section: Bipolar Coordinates and The Fermion Correlatorsmentioning

confidence: 99%

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Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Mondaini¹,

Marino²

2006

J. Phys. A: Math. Gen.

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“…(65). Finally, the first equation of the BBGKY-like hierarchy, written at the order 1/N, gives the evolution of the functionP + (r, t) in the form…”

Section: The Two-body Correlation Functionmentioning

confidence: 99%

Two-dimensional Brownian vortices

Chavanis

2008

Physica A: Statistical Mechanics and its Applications

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We introduce a stochastic model of two-dimensional Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other ("plasma" case) and at negative temperatures, like-sign vortices attract each other ("gravity" case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N -body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N , where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N → +∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N ). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.

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“…The equilibrium statistical mechanics of the neutral TCP is usually studied in the grand canonical ensemble, characterized by the particle fugacities z + = z − = z. The full thermodynamics of this system is known [21,22]. In the stability range of βe 2 < 2, the grand partition function Ξ(z) of the 2D TCP can be turned via the Hubbard-Stratonovich transformation (see, e.g., Ref.…”

Section: Stability Regionmentioning

confidence: 99%

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

Jancovici

Šamaj

2008

J Stat Phys

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A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases.

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Untitled

Cited by 56 publications

References 17 publications

Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Two-dimensional Brownian vortices

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

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