메뉴 건너뛰기




Volumn 238, Issue 1-2, 2003, Pages 257-285

Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable bosons

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037660881     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0851-3     Document Type: Article
Times cited : (54)

References (49)
  • 2
    • 31244437804 scopus 로고    scopus 로고
    • Some identities for determinants of structured matrices
    • Special issue on structured and infinite systems of linear equations
    • Basor, E.L., Ehrhardt, T.: Some identities for determinants of structured matrices. Linear Algebra Appl. 343/344, 5-19 (2002). Special issue on structured and infinite systems of linear equations
    • (2002) Linear Algebra Appl. , vol.343-344 , pp. 5-19
    • Basor, E.L.1    Ehrhardt, T.2
  • 5
    • 0033242958 scopus 로고    scopus 로고
    • On the algebro-geometric integration of the Schlesinger equations
    • Deift, P., Its, A., Kapaev, A., Zhou, X.: On the algebro-geometric integration of the Schlesinger equations. Commun. Math. Phys. 203(3), 613-633 (1999)
    • (1999) Commun. Math. Phys. , vol.203 , Issue.3 , pp. 613-633
    • Deift, P.1    Its, A.2    Kapaev, A.3    Zhou, X.4
  • 7
    • 84949237115 scopus 로고
    • Toeplitz determinants: Some applications, theorems and conjectures
    • Fisher, M.E., Hartwig, R.E.: Toeplitz determinants: some applications, theorems and conjectures. Ad. Chem. Phys. 15, 333-353 (1968)
    • (1968) Ad. Chem. Phys. , vol.15 , pp. 333-353
    • Fisher, M.E.1    Hartwig, R.E.2
  • 10
    • 0035534941 scopus 로고    scopus 로고
    • Application of the τ-function theory of Painlevé equations to random matrices: PIV, PII and the GUE
    • Forrester, P.J., Witte, N.S.: Application of the τ-function theory of Painlevé equations to random matrices: PIV, PII and the GUE. Commun. Math. Phys. 219, 357-398 (2001)
    • (2001) Commun. Math. Phys. , vol.219 , pp. 357-398
    • Forrester, P.J.1    Witte, N.S.2
  • 12
    • 36849136337 scopus 로고
    • Relationship between systems of impenetrable bosons and fermions in one dimension
    • Girardeau, M.D.: Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. 1, 516-523 (1960)
    • (1960) J. Math. Phys. , vol.1 , pp. 516-523
    • Girardeau, M.D.1
  • 13
    • 33646182284 scopus 로고    scopus 로고
    • Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap
    • Girardeau, M.D., Wright, E.M., Triscari, J.M.: Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap. Phys. Rev. A 63, 033601-1-033601-6 (2001)
    • (2001) Phys. Rev. A , vol.63 , pp. 0336011-0336016
    • Girardeau, M.D.1    Wright, E.M.2    Triscari, J.M.3
  • 15
    • 37649033096 scopus 로고    scopus 로고
    • Exploring phase coherence in a 2d lattice of Bose-Einstein condensates
    • Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2d lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87(16), 160405-1-60405-4 (2001)
    • (2001) Phys. Rev. Lett. , vol.87 , Issue.16 , pp. 1604051-1604054
    • Greiner, M.1    Bloch, I.2    Mandel, O.3    Hänsch, T.W.4    Esslinger, T.5
  • 16
    • 0037822355 scopus 로고
    • Asymptotic behavior of Toeplitz matrices and determinants
    • Hartwig, R.E., Fisher, M.E.: Asymptotic behavior of Toeplitz matrices and determinants. Arch. Rational Mech. Anal. 32, 190-225 (1969)
    • (1969) Arch. Rational Mech. Anal. , vol.32 , pp. 190-225
    • Hartwig, R.E.1    Fisher, M.E.2
  • 17
    • 0003175067 scopus 로고
    • Twistor spaces, Einstein metrics and isomonodromic deformations
    • Hitchin, N.J.: Twistor spaces, Einstein metrics and isomonodromic deformations. J. Differ. Geom. 42(1), 30-112 (1995)
    • (1995) J. Differ. Geom. , vol.42 , Issue.1 , pp. 30-112
    • Hitchin, N.J.1
  • 19
    • 0037727538 scopus 로고    scopus 로고
    • Discriminants and functional equations for polynomials orthogonal on the unit circle
    • Ismail, M.E.H., Witte, N.S.: Discriminants and functional equations for polynomials orthogonal on the unit circle. J. Approx. Theory 110(2), 200-228 (2001)
    • (2001) J. Approx. Theory , vol.110 , Issue.2 , pp. 200-228
    • Ismail, M.E.H.1    Witte, N.S.2
  • 21
    • 49049148970 scopus 로고
    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
    • Jimbo, M., Miwa, T.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II. Phys. D 2(3), 407-448 (1981)
    • (1981) Phys. D , vol.2 , Issue.3 , pp. 407-448
    • Jimbo, M.1    Miwa, T.2
  • 22
    • 2342488264 scopus 로고
    • Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
    • Jimbo, M., Miwa, T., Môri, Y., Sato, M.: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1(1), 80-158 (1980)
    • (1980) Phys. D , vol.1 , Issue.1 , pp. 80-158
    • Jimbo, M.1    Miwa, T.2    Môri, Y.3    Sato, M.4
  • 23
    • 0001677729 scopus 로고
    • On Szego's asymptotic formula for Toeplitz determinants and generalizations
    • Johansson, K.: On Szego's asymptotic formula for Toeplitz determinants and generalizations. Bull. Sci. Math. (2) 112(3), 257-304 (1988)
    • (1988) Bull. Sci. Math. (2) , vol.112 , Issue.3 , pp. 257-304
    • Johansson, K.1
  • 24
    • 0031525857 scopus 로고    scopus 로고
    • On random matrices from the compact classical groups
    • Johansson, K.: On random matrices from the compact classical groups. Ann. of Math. (2) 145(3), 519-545(1997)
    • (1997) Ann. of Math. (2) , vol.145 , Issue.3 , pp. 519-545
    • Johansson, K.1
  • 25
    • 0038498600 scopus 로고    scopus 로고
    • Determinant formulas for the Toda and discrete Toda equations
    • solv-inc/9908007
    • Kajiwara, K., Masuda, T., Noumi, M., Ohta, Y., Yamada, Y.: Determinant formulas for the Toda and discrete Toda equations. Funkcialaj Ekvacioj 44, 291-307 (2001). solv-inc/9908007
    • (2001) Funkcialaj Ekvacioj , vol.44 , pp. 291-307
    • Kajiwara, K.1    Masuda, T.2    Noumi, M.3    Ohta, Y.4    Yamada, Y.5
  • 26
    • 1842690428 scopus 로고    scopus 로고
    • On solutions of the Schlesinger equations in terms of θ-functions
    • Kitaev, A.V., Korotkin, D.A.: On solutions of the Schlesinger equations in terms of θ-functions. Internat. Math. Res. Notices (17), 877-905 (1998)
    • (1998) Internat. Math. Res. Notices , Issue.17 , pp. 877-905
    • Kitaev, A.V.1    Korotkin, D.A.2
  • 27
    • 0031206172 scopus 로고    scopus 로고
    • Ground-state correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions
    • Kojima, T.: Ground-state correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions. J. Statist. Phys. 88(3-4), 713-743 (1997)
    • (1997) J. Statist. Phys. , vol.88 , Issue.3-4 , pp. 713-743
    • Kojima, T.1
  • 29
    • 0142053350 scopus 로고
    • Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons
    • Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. J. Math. Phys. 5(7), 930-943 (1964)
    • (1964) J. Math. Phys. , vol.5 , Issue.7 , pp. 930-943
    • Lenard, A.1
  • 30
    • 0000799156 scopus 로고
    • One-dimensional impenetrable bosons in thermal equilibrium
    • Lenard, A.: One-dimensional impenetrable bosons in thermal equilibrium. J. Math. Phys. 7(7), 1268-1272 (1966)
    • (1966) J. Math. Phys. , vol.7 , Issue.7 , pp. 1268-1272
    • Lenard, A.1
  • 31
    • 84972554259 scopus 로고
    • Some remarks on large Toeplitz determinants
    • Lenard, A.: Some remarks on large Toeplitz determinants. Pacific J. Math. 42, 137-145 (1972)
    • (1972) Pacific J. Math. , vol.42 , pp. 137-145
    • Lenard, A.1
  • 32
    • 26344439240 scopus 로고
    • Exact analysis of an interacting Bose gas. I. The general solution and the ground state
    • Lieb, E.H., Liniger, W.: Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev. (2) 130, 1605-1616 (1963)
    • (1963) Phys. Rev. (2) , vol.130 , pp. 1605-1616
    • Lieb, E.H.1    Liniger, W.2
  • 34
    • 0002721417 scopus 로고
    • Sur les équations différentielles du second ordre dont l'intégrale générale a ses points critiques fixes
    • Malmquist, J.: Sur les équations différentielles du second ordre dont l'intégrale générale a ses points critiques fixes. Arkiv Mat. Astron. Fys. 18(8), 1-89 (1922)
    • (1922) Arkiv Mat. Astron. Fys. , vol.18 , Issue.8 , pp. 1-89
    • Malmquist, J.1
  • 39
    • 0001465051 scopus 로고    scopus 로고
    • Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons
    • Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Phys. Rev. Lett. 81(5), 938-941 (1998)
    • (1998) Phys. Rev. Lett. , vol.81 , Issue.5 , pp. 938-941
    • Olshanii, M.1
  • 40
    • 0000476307 scopus 로고
    • Odd symplectic groups
    • Proctor, R.A.: Odd symplectic groups. Invent. Math. 92(2), 307-332 (1988)
    • (1988) Invent. Math. , vol.92 , Issue.2 , pp. 307-332
    • Proctor, R.A.1
  • 41
    • 0003333077 scopus 로고
    • Orthogonal polynomials
    • Providence, Rhode Island: American Mathematical Society, third edition
    • Szegö, G.: Orthogonal Polynomials. Colloquium Publications 23. Providence, Rhode Island: American Mathematical Society, third edition, 1967
    • (1967) Colloquium Publications , vol.23
    • Szegö, G.1
  • 43
    • 0003025563 scopus 로고
    • Fredholm determinants, differential equations and matrix models
    • Tracy, C.A., Widom, H.: Fredholm determinants, differential equations and matrix models. Commun. Math. Phys. 163(1), 33-72 (1994)
    • (1994) Commun. Math. Phys. , vol.163 , Issue.1 , pp. 33-72
    • Tracy, C.A.1    Widom, H.2
  • 44
    • 0002558504 scopus 로고
    • One-particle reduced density matrix of impenetrable bosons in one dimension at zero temperature
    • Vaidya, H.G., Tracy, C.A.: One-particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Phys. Rev. Lett. 42(1), 3-6 (1979)
    • (1979) Phys. Rev. Lett. , vol.42 , Issue.1 , pp. 3-6
    • Vaidya, H.G.1    Tracy, C.A.2
  • 45
    • 36749107330 scopus 로고
    • One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature
    • Vaidya, H.G., Tracy, C.A.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. J. Math. Phys. 20(11), 2291-2312 (1979)
    • (1979) J. Math. Phys. , vol.20 , Issue.11 , pp. 2291-2312
    • Vaidya, H.G.1    Tracy, C.A.2
  • 46
    • 0000920179 scopus 로고
    • Toeplitz determinants with singular generating functions
    • Widom, H.: Toeplitz determinants with singular generating functions. Am. J. Math. 95, 333-383 (1973)
    • (1973) Am. J. Math. , vol.95 , pp. 333-383
    • Widom, H.1
  • 47
    • 0038498602 scopus 로고    scopus 로고
    • New transformations for Painlevé's third transcendent
    • Witte, N.S.: New transformations for Painlevé's third transcendent. To appear Proc. Amer. Math. Soc.
    • Proc. Amer. Math. Soc.
    • Witte, N.S.1
  • 48
    • 0034311207 scopus 로고    scopus 로고
    • Gap probabilities in the finite and scaled Cauchy random matrix ensembles
    • Witte, N.S., Forrester, P.J.: Gap probabilities in the finite and scaled Cauchy random matrix ensembles. Nonl. 13, 1965-1986 (2000)
    • (2000) Nonl. , vol.13 , pp. 1965-1986
    • Witte, N.S.1    Forrester, P.J.2
  • 49
    • 0034258106 scopus 로고    scopus 로고
    • Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles
    • Witte, N.S., Forrester, P.J., Cosgrove, C.M.: Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles. Nonl. 13, 1439-1464 (2000)
    • (2000) Nonl. , vol.13 , pp. 1439-1464
    • Witte, N.S.1    Forrester, P.J.2    Cosgrove, C.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.