Từ tự động hóa tế bào lượng tử đến khí lattice lượng tử

Journal of Statistical Physics - Tập 85 - Trang 551-574 - 1996
David A. Meyer1
1Project in Geometry and Physics, Department of Mathematics, University of California-San Diego, La Jolla

Tóm tắt

Một kiến trúc tự nhiên cho tính toán lượng tử ở quy mô nano là tự động hóa tế bào lượng tử. Dựa trên quan sát này, chúng tôi bắt đầu một cuộc điều tra về tự động hóa tế bào đơn vị chính xác. Sau khi chứng minh rằng không thể có tự động hóa tế bào vô ích, đồng nhất, địa phương, đơn vị, vô hướng trong một chiều, chúng tôi làm yếu đi điều kiện đồng nhất và chỉ ra rằng có các tự động hóa tế bào phân vùng, đơn vị, không tầm thường. Chúng tôi tìm thấy một họ quy tắc tiến hóa một tham số mà có thể được hiểu tốt nhất như là quy tắc cho một tự động hóa lượng tử một hạt. Mô hình này được trình bày lại một cách tự nhiên dưới dạng một tự động hóa tế bào hai thành phần mà chúng tôi chứng minh rằng hạn chế đến phương trình Dirac. Chúng tôi mô tả hai sự tổng quát của tự động hóa này, trong đó sự tổng quát thứ hai, cho nhiều hạt tương tác, là định nghĩa chính xác của một khí lattice lượng tử.

Từ khóa


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Journal of Statistical Physics

Tập 85

551-574

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